Data Preprocessing and Exploratory Data Analysis
#Step one: explore reported new cases data near sewage plant with possibility
#to create a model that represents the whole population?
#use NC reported cases data?....
reported_cases <- read_excel("New_Cases_Per_10K_updated_in_wwtp.xlsx")
glimpse(reported_cases)
## Rows: 9,815
## Columns: 6
## $ Index <chr> "1", "2", "3", "4", "5", "6", "7", "8",…
## $ `Wastewater Treatment Plant` <chr> "Cary 1", "Cary 1", "Cary 1", "Cary 1",…
## $ County <chr> "Wake", "Wake", "Wake", "Wake", "Wake",…
## $ Date <chr> "5/25/2022", "5/24/2022", "5/23/2022", …
## $ `Population Served` <dbl> 84189, 84189, 84189, 84189, 84189, 8418…
## $ `New Cases Per 10,000 Persons` <dbl> NA, NA, 2.02, 3.21, 7.36, 7.84, 9.15, 7…
colnames(reported_cases)[2] <- "wwtp"
colnames(reported_cases)[5] <- "population"
colnames(reported_cases)[6] <- "new_cases_per_10k"
glimpse(reported_cases)
## Rows: 9,815
## Columns: 6
## $ Index <chr> "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "…
## $ wwtp <chr> "Cary 1", "Cary 1", "Cary 1", "Cary 1", "Cary 1", "C…
## $ County <chr> "Wake", "Wake", "Wake", "Wake", "Wake", "Wake", "Wak…
## $ Date <chr> "5/25/2022", "5/24/2022", "5/23/2022", "5/22/2022", …
## $ population <dbl> 84189, 84189, 84189, 84189, 84189, 84189, 84189, 841…
## $ new_cases_per_10k <dbl> NA, NA, 2.02, 3.21, 7.36, 7.84, 9.15, 7.72, 7.25, 3.…
reported_cases <- reported_cases %>% arrange(mdy(reported_cases$Date))
reported_cases$Date <- mdy(reported_cases$Date)
table(reported_cases$County)
##
## Buncombe,Henderson Carteret Chatham Cumberland
## 355 736 143 355
## Durham Forsyth Guilford Halifax,Northampton
## 508 355 356 355
## Jackson Mcdowell Mecklenburg New Hanover
## 508 357 1375 1011
## Onslow Orange Pitt Scotland
## 82 508 508 357
## Wake Wilson
## 1585 355
png(filename="new_cases_plot.png", res = 500,units = "cm", width = 20, height = 10)
na.omit(reported_cases) %>% ggplot(aes(Date,new_cases_per_10k)) + facet_wrap(~County) + geom_line() +
ylab("New COVID-19 cases per 10K") + theme_bw()
dev.off()
## quartz_off_screen
## 2
png(filename="log_new_cases_boxplot.png", res = 500,units = "cm", width = 20, height = 12)
na.omit(reported_cases) %>% ggplot(aes(County,log(new_cases_per_10k))) +
geom_boxplot() + ylab("Logarithm of new COVID-19 cases per 10k") +
theme_bw() + theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
dev.off()
## quartz_off_screen
## 2
#Wake: New Cases
wake_reported_cases <- subset(reported_cases,County=="Wake")
glimpse(wake_reported_cases)
## Rows: 1,585
## Columns: 6
## $ Index <chr> "6,611", "6,610", "6,609", "6,608", "6,607", "6,606"…
## $ wwtp <chr> "Raleigh", "Raleigh", "Raleigh", "Raleigh", "Raleigh…
## $ County <chr> "Wake", "Wake", "Wake", "Wake", "Wake", "Wake", "Wak…
## $ Date <date> 2021-01-03, 2021-01-04, 2021-01-05, 2021-01-06, 202…
## $ population <dbl> 550000, 550000, 550000, 550000, 550000, 550000, 5500…
## $ new_cases_per_10k <dbl> 8.76, 3.15, 13.69, 10.56, 11.00, 11.16, 8.64, 5.29, …
summary(wake_reported_cases)
## Index wwtp County Date
## Length:1585 Length:1585 Length:1585 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-11-08
## Mode :character Mode :character Mode :character Median :2022-01-13
## Mean :2021-12-21
## 3rd Qu.:2022-03-20
## Max. :2022-05-25
##
## population new_cases_per_10k
## Min. : 7776 Min. : 0.040
## 1st Qu.: 30655 1st Qu.: 1.310
## Median : 75886 Median : 2.570
## Mean :212196 Mean : 7.511
## 3rd Qu.:550000 3rd Qu.: 6.430
## Max. :550000 Max. :109.310
## NA's :75
which(is.na(wake_reported_cases$`New Cases Per 10,000 Persons`))
## integer(0)
wake_reported_cases %>% slice_min(new_cases_per_10k)
## # A tibble: 1 × 6
## Index wwtp County Date population new_cases_per_10k
## <chr> <chr> <chr> <date> <dbl> <dbl>
## 1 6,428 Raleigh Wake 2021-07-05 550000 0.04
wake_reported_cases %>% slice_max(new_cases_per_10k)
## # A tibble: 1 × 6
## Index wwtp County Date population new_cases_per_10k
## <chr> <chr> <chr> <date> <dbl> <dbl>
## 1 6,983 Raleigh 3 Wake 2022-01-05 7776 109.
wake_reported_cases$new_cases_per_10k <- LOCF(wake_reported_cases$new_cases_per_10k)
summary(wake_reported_cases)
## Index wwtp County Date
## Length:1585 Length:1585 Length:1585 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-11-08
## Mode :character Mode :character Mode :character Median :2022-01-13
## Mean :2021-12-21
## 3rd Qu.:2022-03-20
## Max. :2022-05-25
## population new_cases_per_10k
## Min. : 7776 Min. : 0.040
## 1st Qu.: 30655 1st Qu.: 1.160
## Median : 75886 Median : 2.570
## Mean :212196 Mean : 7.217
## 3rd Qu.:550000 3rd Qu.: 6.200
## Max. :550000 Max. :109.310
df_wake <- wake_reported_cases %>% group_by(Date) %>% summarise(mean_new_cases=mean(new_cases_per_10k))
summary(df_wake)
## Date mean_new_cases
## Min. :2021-01-03 Min. : 0.040
## 1st Qu.:2021-05-09 1st Qu.: 1.175
## Median :2021-09-13 Median : 2.390
## Mean :2021-09-13 Mean : 5.049
## 3rd Qu.:2022-01-18 3rd Qu.: 4.559
## Max. :2022-05-25 Max. :65.640
#Wake: wastewater viral gene copies
wastewater_data <- read_excel("wastewater_data_updated.xlsx")
glimpse(wastewater_data)
## Rows: 2,554
## Columns: 7
## $ Index <chr> "1", "2", "3", "4", "5", "6", "7", "8",…
## $ `Wastewater Treatment Plant` <chr> "Cary 1", "Cary 1", "Cary 1", "Cary 1",…
## $ County <chr> "Wake", "Wake", "Wake", "Wake", "Wake",…
## $ Date <chr> "5/24/2022", "5/19/2022", "5/17/2022", …
## $ `Population Served` <dbl> 84189, 84189, 84189, 84189, 84189, 8418…
## $ `Viral Gene Copies Per Person` <dbl> 27231850.1, 41893904.5, 24733220.3, 216…
## $ `Viral Gene Copies/L` <dbl> 72706.915, 138858.315, 71905.615, 71604…
wastewater_data <- wastewater_data%>% arrange(mdy(wastewater_data$Date))
wastewater_data$Date <- mdy(wastewater_data$Date)
colnames(wastewater_data)[2]<-"wwtp"
colnames(wastewater_data)[5]<-"population"
colnames(wastewater_data)[6]<-"viral_gene_copies_per_person"
colnames(wastewater_data)[7]<-"viral_gene_copies/L"
summary(wastewater_data) #no missing values
## Index wwtp County Date
## Length:2554 Length:2554 Length:2554 Min. :2021-01-04
## Class :character Class :character Class :character 1st Qu.:2021-07-10
## Mode :character Mode :character Mode :character Median :2021-11-06
## Mean :2021-10-23
## 3rd Qu.:2022-02-23
## Max. :2022-05-25
## population viral_gene_copies_per_person viral_gene_copies/L
## Min. : 3500 Min. : 39617 Min. : 0
## 1st Qu.: 15527 1st Qu.: 1219550 1st Qu.: 3536
## Median : 74331 Median : 5043606 Median : 13325
## Mean : 99804 Mean : 14331526 Mean : 38399
## 3rd Qu.:120000 3rd Qu.: 14409756 3rd Qu.: 37871
## Max. :550000 Max. :861501758 Max. :2646342
png(filename="viral_gene_plot.png", res = 500,units = "cm", width = 20, height = 10)
wastewater_data %>% ggplot(aes(Date,viral_gene_copies_per_person)) + geom_line() +
facet_wrap(~ County) + theme_bw() + ylab("Viral gene copies per person")
dev.off()
## quartz_off_screen
## 2
png(filename="log_viral_gene_boxplot.png", res = 500,units = "cm", width = 20, height = 10)
wastewater_data %>% ggplot(aes(County,log(viral_gene_copies_per_person))) + geom_boxplot() +
theme_bw() + theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
ylab("log(Viral gene copies per person)")
dev.off()
## quartz_off_screen
## 2
wake_wastewater_data <- wastewater_data %>% dplyr::filter(County=='Wake')
summary(wake_wastewater_data)
## Index wwtp County Date
## Length:389 Length:389 Length:389 Min. :2021-01-06
## Class :character Class :character Class :character 1st Qu.:2021-11-18
## Mode :character Mode :character Mode :character Median :2022-01-28
## Mean :2021-12-28
## 3rd Qu.:2022-03-29
## Max. :2022-05-25
## population viral_gene_copies_per_person viral_gene_copies/L
## Min. : 7776 Min. : 90179 Min. : 0
## 1st Qu.: 30655 1st Qu.: 2263004 1st Qu.: 7030
## Median : 75886 Median : 6776605 Median : 20494
## Mean :218051 Mean : 20720759 Mean : 61134
## 3rd Qu.:550000 3rd Qu.: 18414486 3rd Qu.: 59674
## Max. :550000 Max. :861501758 Max. :2646342
wake_wastewater_data %>% slice_min(viral_gene_copies_per_person)
## # A tibble: 1 × 7
## Index wwtp County Date population viral_gene_copies… `viral_gene_co…`
## <chr> <chr> <chr> <date> <dbl> <dbl> <dbl>
## 1 1,696 Raleigh Wake 2021-05-08 550000 90179. 0
wake_wastewater_data %>% slice_max(viral_gene_copies_per_person)
## # A tibble: 1 × 7
## Index wwtp County Date population viral_gene_copies… `viral_gene_co…`
## <chr> <chr> <chr> <date> <dbl> <dbl> <dbl>
## 1 1,638 Raleigh Wake 2022-01-14 550000 861501758. 2646342.
png(filename="viral_gene_plot_wake.png", res = 500,units = "cm", width = 20, height = 10)
wake_wastewater_data %>% ggplot(aes(Date,viral_gene_copies_per_person)) + geom_line() +
facet_wrap(~ wwtp) + theme_bw(base_size = 16) + ylab("Viral gene copies per person")
dev.off()
## quartz_off_screen
## 2
png(filename="log_viral_gene_plot_wake.png", res = 500,units = "cm", width = 20, height = 10)
wake_wastewater_data %>% ggplot(aes(wwtp,log(viral_gene_copies_per_person))) +
geom_boxplot() + theme_bw(base_size = 16) +
ylab("Log(viral gene copies per person)") +
xlab("Wastewater treatment plants")
dev.off()
## quartz_off_screen
## 2
average_wake_wastewater <- wake_wastewater_data %>% group_by(Date) %>%
summarise(mean_viral_gene_copies_per_person = mean(viral_gene_copies_per_person))
average_wake_wastewater
## # A tibble: 188 × 2
## Date mean_viral_gene_copies_per_person
## <date> <dbl>
## 1 2021-01-06 24940866.
## 2 2021-01-09 13086649.
## 3 2021-01-13 20010814.
## 4 2021-01-16 15455316.
## 5 2021-01-20 8641657.
## 6 2021-01-23 9986540.
## 7 2021-01-27 11114735.
## 8 2021-01-30 2670705.
## 9 2021-02-03 5430043.
## 10 2021-02-13 7822743.
## # … with 178 more rows
full_average_wake_wastewater <- pad(average_wake_wastewater,start_val = as.Date('2021-01-04'),
end_val = as.Date('2022-05-25'))
full_average_wake_wastewater <- full_average_wake_wastewater %>%
mutate(full_viral_gene_copies_per_person = na_locf(mean_viral_gene_copies_per_person))
full_average_wake_wastewater %>% ggplot(aes(Date,full_viral_gene_copies_per_person)) + geom_line()
full_average_wake_wastewater <- full_average_wake_wastewater %>% select(Date,full_viral_gene_copies_per_person)
summary(full_average_wake_wastewater)
## Date full_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 90179
## 1st Qu.:2021-05-10 1st Qu.: 1587873
## Median :2021-09-14 Median : 5055290
## Mean :2021-09-14 Mean : 20579092
## 3rd Qu.:2022-01-18 3rd Qu.: 12713191
## Max. :2022-05-25 Max. :861501758
#Wake: merged data
full_cases_wastewater_data <- merge(df_wake[-1,],full_average_wake_wastewater,by="Date")
summary(full_cases_wastewater_data )
## Date mean_new_cases full_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 0.040 Min. : 90179
## 1st Qu.:2021-05-10 1st Qu.: 1.170 1st Qu.: 1587873
## Median :2021-09-14 Median : 2.380 Median : 5055290
## Mean :2021-09-14 Mean : 5.042 Mean : 20579092
## 3rd Qu.:2022-01-18 3rd Qu.: 4.554 3rd Qu.: 12713191
## Max. :2022-05-25 Max. :65.640 Max. :861501758
which.min(full_cases_wastewater_data$mean_new_cases)
## [1] 183
full_cases_wastewater_data[183,]
## Date mean_new_cases full_viral_gene_copies_per_person
## 183 2021-07-05 0.04 1587873
which.min(full_cases_wastewater_data$full_viral_gene_copies_per_person)
## [1] 125
full_cases_wastewater_data[125,] #minimum covid-19 prevalence within same season
## Date mean_new_cases full_viral_gene_copies_per_person
## 125 2021-05-08 1.33 90179.23
which.max(full_cases_wastewater_data$mean_new_cases)
## [1] 367
full_cases_wastewater_data[367,]
## Date mean_new_cases full_viral_gene_copies_per_person
## 367 2022-01-05 65.64 46312926
which.max(full_cases_wastewater_data$full_viral_gene_copies_per_person)
## [1] 376
full_cases_wastewater_data[376,] #maximum covid-19 prevalence within same month
## Date mean_new_cases full_viral_gene_copies_per_person
## 376 2022-01-14 47.66167 861501758
#Mecklenburg: covid_cases
mecklenburg_reported_cases <- subset(reported_cases,County=="Mecklenburg")
glimpse(mecklenburg_reported_cases)
## Rows: 1,375
## Columns: 6
## $ Index <chr> "1,631", "2,139", "1,630", "2,138", "1,629", "2,137"…
## $ wwtp <chr> "Charlotte 1", "Charlotte 2", "Charlotte 1", "Charlo…
## $ County <chr> "Mecklenburg", "Mecklenburg", "Mecklenburg", "Meckle…
## $ Date <date> 2021-01-03, 2021-01-03, 2021-01-04, 2021-01-04, 202…
## $ population <dbl> 68685, 182501, 68685, 182501, 68685, 182501, 68685, …
## $ new_cases_per_10k <dbl> 7.86, 5.53, 6.99, 4.11, 13.25, 10.47, 9.46, 7.23, 8.…
summary(mecklenburg_reported_cases)
## Index wwtp County Date
## Length:1375 Length:1375 Length:1375 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-06-16
## Mode :character Mode :character Mode :character Median :2021-10-08
## Mean :2021-10-02
## 3rd Qu.:2022-01-31
## Max. :2022-05-25
##
## population new_cases_per_10k
## Min. : 68685 Min. : 0.110
## 1st Qu.: 68685 1st Qu.: 0.990
## Median :120000 Median : 2.040
## Mean :124133 Mean : 3.982
## 3rd Qu.:182501 3rd Qu.: 4.330
## Max. :182501 Max. :47.580
## NA's :10
mecklenburg_reported_cases$new_cases_per_10k <- LOCF(mecklenburg_reported_cases$new_cases_per_10k)
df_mecklenburg <- mecklenburg_reported_cases %>% group_by(Date) %>% summarise(mean_new_cases =
mean(new_cases_per_10k))
summary(df_mecklenburg[-1,])
## Date mean_new_cases
## Min. :2021-01-04 Min. : 0.190
## 1st Qu.:2021-05-10 1st Qu.: 1.048
## Median :2021-09-14 Median : 2.070
## Mean :2021-09-14 Mean : 3.816
## 3rd Qu.:2022-01-18 3rd Qu.: 4.085
## Max. :2022-05-25 Max. :38.407
#Mecklenburg: wastewater viral gene copies
mecklenburg_wastewater_data <- wastewater_data %>% dplyr::filter(County=='Mecklenburg')
summary(mecklenburg_wastewater_data)
## Index wwtp County Date
## Length:357 Length:357 Length:357 Min. :2021-01-04
## Class :character Class :character Class :character 1st Qu.:2021-06-11
## Mode :character Mode :character Mode :character Median :2021-10-02
## Mean :2021-09-29
## 3rd Qu.:2022-02-05
## Max. :2022-05-24
## population viral_gene_copies_per_person viral_gene_copies/L
## Min. : 68685 Min. : 72703 Min. : 0
## 1st Qu.: 68685 1st Qu.: 3178201 1st Qu.: 10238
## Median :120000 Median : 7729720 Median : 24749
## Mean :124630 Mean : 16956243 Mean : 54897
## 3rd Qu.:182501 3rd Qu.: 19772480 3rd Qu.: 62500
## Max. :182501 Max. :379065946 Max. :1101437
png(filename="viral_gene_plot_meck.png", res = 500,units = "cm", width = 20, height = 10)
mecklenburg_wastewater_data%>% ggplot(aes(Date,viral_gene_copies_per_person)) + geom_line() +
facet_wrap(~ wwtp) + theme_bw(base_size = 16) + ylab("Viral gene copies per person")
dev.off()
## quartz_off_screen
## 2
png(filename="log_viral_gene_plot_meck.png", res = 500,units = "cm", width = 20, height = 10)
mecklenburg_wastewater_data %>% ggplot(aes(wwtp,log(viral_gene_copies_per_person))) +
geom_boxplot()+ theme_bw(base_size = 16) +
ylab("Log(viral gene copies per person)") +xlab("Wastewater treatment plants")
dev.off()
## quartz_off_screen
## 2
average_meck_wastewater <- mecklenburg_wastewater_data %>% group_by(Date) %>%
summarise(mean_viral_gene_copies_per_person = mean(viral_gene_copies_per_person))
average_meck_wastewater
## # A tibble: 152 × 2
## Date mean_viral_gene_copies_per_person
## <date> <dbl>
## 1 2021-01-04 48863073.
## 2 2021-01-05 16458455.
## 3 2021-01-06 28467455.
## 4 2021-01-11 11486856.
## 5 2021-01-12 19831661.
## 6 2021-01-13 22175968.
## 7 2021-01-20 13991321.
## 8 2021-01-25 18933735.
## 9 2021-01-27 12279871.
## 10 2021-02-01 4781264.
## # … with 142 more rows
full_average_meck_wastewater <- pad(average_meck_wastewater,start_val = as.Date('2021-01-04'),
end_val = as.Date('2022-05-25'))
full_average_meck_wastewater <- full_average_meck_wastewater %>%
mutate(full_viral_gene_copies_per_person = na_locf(mean_viral_gene_copies_per_person))
full_average_meck_wastewater%>% ggplot(aes(Date,full_viral_gene_copies_per_person)) +
geom_line()
full_average_wake_wastewater <- full_average_meck_wastewater %>% select(Date,full_viral_gene_copies_per_person)
summary(full_average_meck_wastewater)
## Date mean_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 283193
## 1st Qu.:2021-05-10 1st Qu.: 3821535
## Median :2021-09-14 Median : 7985329
## Mean :2021-09-14 Mean : 18052981
## 3rd Qu.:2022-01-18 3rd Qu.: 20257270
## Max. :2022-05-25 Max. :379065946
## NA's :355
## full_viral_gene_copies_per_person
## Min. : 283193
## 1st Qu.: 3818869
## Median : 8040114
## Mean : 16676303
## 3rd Qu.: 19388197
## Max. :379065946
##
#Mecklenburg: merged data
full_cases_wastewater_data_meck <- merge(df_mecklenburg,full_average_meck_wastewater,by="Date")
summary(full_cases_wastewater_data_meck)
## Date mean_new_cases mean_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 0.190 Min. : 283193
## 1st Qu.:2021-05-10 1st Qu.: 1.048 1st Qu.: 3821535
## Median :2021-09-14 Median : 2.070 Median : 7985329
## Mean :2021-09-14 Mean : 3.816 Mean : 18052981
## 3rd Qu.:2022-01-18 3rd Qu.: 4.085 3rd Qu.: 20257270
## Max. :2022-05-25 Max. :38.407 Max. :379065946
## NA's :355
## full_viral_gene_copies_per_person
## Min. : 283193
## 1st Qu.: 3818869
## Median : 8040114
## Mean : 16676303
## 3rd Qu.: 19388197
## Max. :379065946
##
which.min(full_cases_wastewater_data_meck$mean_new_cases)
## [1] 155
full_cases_wastewater_data_meck[155,]
## Date mean_new_cases mean_viral_gene_copies_per_person
## 155 2021-06-07 0.19 2105482
## full_viral_gene_copies_per_person
## 155 2105482
which.min(full_cases_wastewater_data_meck$full_viral_gene_copies_per_person)
## [1] 66
full_cases_wastewater_data_meck[66,] #minimum covid-19 prevalence not in the same period.....
## Date mean_new_cases mean_viral_gene_copies_per_person
## 66 2021-03-10 1.695 283192.9
## full_viral_gene_copies_per_person
## 66 283192.9
which.max(full_cases_wastewater_data_meck$mean_new_cases)
## [1] 368
full_cases_wastewater_data_meck[368,]
## Date mean_new_cases mean_viral_gene_copies_per_person
## 368 2022-01-06 38.40667 NA
## full_viral_gene_copies_per_person
## 368 125299582
which.max(full_cases_wastewater_data_meck$full_viral_gene_copies_per_person)
## [1] 369
full_cases_wastewater_data_meck[369,] #maximum covid-19 prevalence within same month, reflecting the peak
## Date mean_new_cases mean_viral_gene_copies_per_person
## 369 2022-01-07 33.34667 379065946
## full_viral_gene_copies_per_person
## 369 379065946
#New Hanover: covid cases
new_hanover_reported_cases <- subset(reported_cases,County=="New Hanover")
glimpse(new_hanover_reported_cases)
## Rows: 1,011
## Columns: 6
## $ Index <chr> "9,460", "9,459", "9,458", "9,457", "9,456", "5,726"…
## $ wwtp <chr> "Wilmington City", "Wilmington City", "Wilmington Ci…
## $ County <chr> "New Hanover", "New Hanover", "New Hanover", "New Ha…
## $ Date <date> 2021-01-03, 2021-01-04, 2021-01-05, 2021-01-06, 202…
## $ population <dbl> 58361, 58361, 58361, 58361, 58361, 67743, 58361, 677…
## $ new_cases_per_10k <dbl> 4.63, 3.77, 9.42, 8.22, 7.20, 6.05, 5.48, 6.64, 4.80…
summary(new_hanover_reported_cases)
## Index wwtp County Date
## Length:1011 Length:1011 Length:1011 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-05-11
## Mode :character Mode :character Mode :character Median :2021-09-15
## Mean :2021-09-14
## 3rd Qu.:2022-01-19
## Max. :2022-05-25
##
## population new_cases_per_10k
## Min. :58361 Min. : 0.300
## 1st Qu.:58361 1st Qu.: 0.340
## Median :58361 Median : 1.710
## Mean :63029 Mean : 3.529
## 3rd Qu.:67743 3rd Qu.: 3.600
## Max. :67743 Max. :48.490
## NA's :37
new_hanover_reported_cases$new_cases_per_10k <- LOCF(new_hanover_reported_cases$new_cases_per_10k)
summary(new_hanover_reported_cases)
## Index wwtp County Date
## Length:1011 Length:1011 Length:1011 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-05-11
## Mode :character Mode :character Mode :character Median :2021-09-15
## Mean :2021-09-14
## 3rd Qu.:2022-01-19
## Max. :2022-05-25
## population new_cases_per_10k
## Min. :58361 Min. : 0.300
## 1st Qu.:58361 1st Qu.: 0.340
## Median :58361 Median : 1.540
## Mean :63029 Mean : 3.412
## 3rd Qu.:67743 3rd Qu.: 3.430
## Max. :67743 Max. :48.490
df_new_hanover <- new_hanover_reported_cases %>% group_by(Date) %>%
summarise(mean_new_cases = mean(new_cases_per_10k))
summary(df_new_hanover[-1,])
## Date mean_new_cases
## Min. :2021-01-04 Min. : 0.300
## 1st Qu.:2021-05-10 1st Qu.: 0.580
## Median :2021-09-14 Median : 1.680
## Mean :2021-09-14 Mean : 3.426
## 3rd Qu.:2022-01-18 3rd Qu.: 3.580
## Max. :2022-05-25 Max. :37.870
#New Hanover: wastewater viral gene copies per person
new_hanover_wastewater_data <- wastewater_data %>% dplyr::filter(County=='New Hanover')
png(filename="viral_gene_plot_hanover.png", res = 500,units = "cm", width = 20, height = 10)
new_hanover_wastewater_data%>% ggplot(aes(Date,viral_gene_copies_per_person)) + geom_line() +
facet_wrap(~ wwtp) + theme_bw(base_size = 16) + ylab("Viral gene copies per person")
dev.off()
## quartz_off_screen
## 2
png(filename="log_viral_gene_plot_hanover.png", res = 500,units = "cm", width = 20, height = 10)
new_hanover_wastewater_data %>% ggplot(aes(wwtp,log(viral_gene_copies_per_person))) +
geom_boxplot() + theme_bw(base_size = 16) + xlab("Log(viral gene copies per person)")
dev.off()
## quartz_off_screen
## 2
average_hanover_wastewater <- new_hanover_wastewater_data %>% group_by(Date) %>%
summarise(mean_viral_gene_copies_per_person = mean(viral_gene_copies_per_person))
full_average_hanover_wastewater <- pad(average_hanover_wastewater,start_val = as.Date('2021-01-04'),
end_val = as.Date('2022-05-25'))
full_average_hanover_wastewater <- full_average_hanover_wastewater %>%
mutate(full_viral_gene_copies_per_person = na_locf(mean_viral_gene_copies_per_person))
average_hanover_wastewater %>% ggplot(aes(Date,mean_viral_gene_copies_per_person)) + geom_line()
full_average_hanover_wastewater <- full_average_hanover_wastewater %>% select(Date,full_viral_gene_copies_per_person)
summary(full_average_hanover_wastewater)
## Date full_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 74540
## 1st Qu.:2021-05-10 1st Qu.: 834407
## Median :2021-09-14 Median : 3676553
## Mean :2021-09-14 Mean : 8561704
## 3rd Qu.:2022-01-18 3rd Qu.: 8560494
## Max. :2022-05-25 Max. :74023842
#New Hanover: Merged Data
full_cases_wastewater_data_hanover <- merge(df_new_hanover[-1,],full_average_hanover_wastewater,by="Date")
summary(full_cases_wastewater_data_hanover)
## Date mean_new_cases full_viral_gene_copies_per_person
## Min. :2021-01-04 Min. : 0.300 Min. : 74540
## 1st Qu.:2021-05-10 1st Qu.: 0.580 1st Qu.: 834407
## Median :2021-09-14 Median : 1.680 Median : 3676553
## Mean :2021-09-14 Mean : 3.426 Mean : 8561704
## 3rd Qu.:2022-01-18 3rd Qu.: 3.580 3rd Qu.: 8560494
## Max. :2022-05-25 Max. :37.870 Max. :74023842
which.min(full_cases_wastewater_data_hanover$mean_new_cases)
## [1] 141
full_cases_wastewater_data_meck[141,]
## Date mean_new_cases mean_viral_gene_copies_per_person
## 141 2021-05-24 0.365 306292.8
## full_viral_gene_copies_per_person
## 141 306292.8
which.min(full_cases_wastewater_data_hanover$full_viral_gene_copies_per_person)
## [1] 124
full_cases_wastewater_data_meck[124,] #minimum covid-19 prevalence in the same period.....
## Date mean_new_cases mean_viral_gene_copies_per_person
## 124 2021-05-07 0.805 NA
## full_viral_gene_copies_per_person
## 124 5860626
which.max(full_cases_wastewater_data_hanover$mean_new_cases)
## [1] 382
full_cases_wastewater_data_meck[382,]
## Date mean_new_cases mean_viral_gene_copies_per_person
## 382 2022-01-20 26.45333 NA
## full_viral_gene_copies_per_person
## 382 94292358
which.max(full_cases_wastewater_data_hanover$full_viral_gene_copies_per_person)
## [1] 384
full_cases_wastewater_data_meck[384,] #maximum covid-19 prevalence within same month, reflecting the peak
## Date mean_new_cases mean_viral_gene_copies_per_person
## 384 2022-01-22 14.81333 71015872
## full_viral_gene_copies_per_person
## 384 71015872
#plot of wake, meck and new hanover#
png(filename = "cases_analysis.png", units = "cm", res = 700,
width = 20, height = 10)
full_cases_wastewater_data %>% ggplot(aes(Date,mean_new_cases)) +
geom_line(aes(color="Wake")) +
geom_line(data = full_cases_wastewater_data_meck,
aes(Date,mean_new_cases, color="Mecklenburg")) +
geom_line(data = full_cases_wastewater_data_hanover,
aes(Date,mean_new_cases, color="New Hanover")) +
scale_colour_manual(values=c("Wake"="mediumseagreen", "Mecklenburg"="mediumpurple1",
"New Hanover"="maroon1"),
labels=c("Wake", "Mecklenburg", "New Hanover")) + theme_bw() +
ylab("New COVID-19 cases") + theme(legend.position = "bottom")
dev.off()
## quartz_off_screen
## 2
png(filename = "wastewater_analysis.png", units = "cm", res = 700,
width = 20, height = 10)
full_cases_wastewater_data %>% ggplot(aes(Date,full_viral_gene_copies_per_person)) +
geom_line(aes(color="Wake")) +
geom_line(data = full_cases_wastewater_data_meck,
aes(Date,full_viral_gene_copies_per_person, color="Mecklenburg")) +
geom_line(data = full_cases_wastewater_data_hanover,
aes(Date,full_viral_gene_copies_per_person, color="New Hanover")) +
scale_colour_manual(values=c("Wake"="mediumseagreen", "Mecklenburg"="mediumpurple1",
"New Hanover"="maroon1"),
labels=c("Wake", "Mecklenburg", "New Hanover")) + theme_bw() +
ylab("Viral gene copies per person") + theme(legend.position = "bottom")
dev.off()
## quartz_off_screen
## 2
#Weather properties that affect wastewater#
#Wake weather: data preprocessing#
wake_weather <- read.csv("wake_weather.csv")
glimpse(wake_weather)
## Rows: 32,854
## Columns: 8
## $ STATION <chr> "US1NCWK0022", "US1NCWK0022", "US1NCWK0022", "US1NCWK0022", "U…
## $ NAME <chr> "APEX 6.1 ESE, NC US", "APEX 6.1 ESE, NC US", "APEX 6.1 ESE, N…
## $ DATE <chr> "2021-01-04", "2021-01-05", "2021-01-06", "2021-01-07", "2021-…
## $ PRCP <dbl> 0.03, 0.00, 0.00, 0.00, 0.26, 0.45, 0.00, 0.00, 0.15, 0.05, 0.…
## $ TAVG <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TMAX <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TMIN <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TOBS <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
sum(is.na(wake_weather$PRCP)) #757 NA, assume no rain...
## [1] 757
#which(is.na(wake_weather$PRCP))
wake_weather <-
wake_weather %>% mutate(PRCP = replace_na(PRCP,mean(PRCP,na.rm=TRUE)))
wake_weather_prcp <- wake_weather %>% group_by(DATE) %>% summarise(mean_precipation = mean(PRCP))
sum(is.na(wake_weather$TAVG))
## [1] 32347
sum(is.na(wake_weather$TMIN))
## [1] 29389
sum(is.na(wake_weather$TMAX))
## [1] 29371
sum(is.na(wake_weather$TOBS))
## [1] 29886
#temperature is the same in all towns within Wake
full_tavg_data <- wake_weather[complete.cases(wake_weather$TAVG),]
table(full_tavg_data$STATION) #only one stations
##
## USW00013722
## 507
wake_temp <- full_tavg_data %>% select(DATE,TAVG)
wake_weather <- merge(wake_weather_prcp,wake_temp,order.by=DATE)
summary(wake_weather)
## DATE mean_precipation TAVG
## Length:507 Min. :0.000000 Min. :25.00
## Class :character 1st Qu.:0.002439 1st Qu.:46.50
## Mode :character Median :0.009689 Median :61.00
## Mean :0.130198 Mean :59.61
## 3rd Qu.:0.092545 3rd Qu.:72.00
## Max. :2.855180 Max. :86.00
wake_weather$DATE <- as.Date(wake_weather$DATE)
summary(wake_weather)
## DATE mean_precipation TAVG
## Min. :2021-01-04 Min. :0.000000 Min. :25.00
## 1st Qu.:2021-05-10 1st Qu.:0.002439 1st Qu.:46.50
## Median :2021-09-14 Median :0.009689 Median :61.00
## Mean :2021-09-14 Mean :0.130198 Mean :59.61
## 3rd Qu.:2022-01-18 3rd Qu.:0.092545 3rd Qu.:72.00
## Max. :2022-05-25 Max. :2.855180 Max. :86.00
colnames(wake_weather)[1]<-"Date"
#mecklenburg weather: data preprocessing#
meck_weather <- read.csv("mecklenburg_weather.csv")
glimpse(meck_weather)
## Rows: 6,940
## Columns: 7
## $ STATION <chr> "US1NCMK0053", "US1NCMK0053", "US1NCMK0053", "US1NCMK0053", "U…
## $ NAME <chr> "CHARLOTTE 7.0 ENE, NC US", "CHARLOTTE 7.0 ENE, NC US", "CHARL…
## $ DATE <chr> "2021-01-04", "2021-01-05", "2021-01-06", "2021-01-07", "2021-…
## $ PRCP <dbl> 0.01, 0.00, 0.04, 0.00, 0.81, 0.00, 0.00, 0.00, 0.00, 0.00, 0.…
## $ TAVG <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TMAX <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TMIN <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
sum(is.na(meck_weather$PRCP))
## [1] 86
meck_weather <-
meck_weather %>% mutate(PRCP = replace_na(PRCP,mean(PRCP,na.rm=TRUE)))
meck_weather_prcp <- meck_weather %>% group_by(DATE) %>% summarise(mean_precipation = mean(PRCP))
meck_weather_prcp
## # A tibble: 507 × 2
## DATE mean_precipation
## <chr> <dbl>
## 1 2021-01-04 0.00231
## 2 2021-01-05 0.0123
## 3 2021-01-06 0.0192
## 4 2021-01-07 0.0265
## 5 2021-01-08 0.505
## 6 2021-01-09 0.28
## 7 2021-01-10 0
## 8 2021-01-11 0.00786
## 9 2021-01-12 0.147
## 10 2021-01-13 0.0315
## # … with 497 more rows
sum(is.na(meck_weather$TAVG))
## [1] 6433
full_tavg_data_meck <- meck_weather[complete.cases(meck_weather$TAVG),]
table(full_tavg_data_meck$STATION)
##
## USW00013881
## 507
meck_temp <- full_tavg_data_meck %>% select(DATE,TAVG)
meck_weather <- merge(meck_weather_prcp,meck_temp, order.by=DATE)
meck_weather$DATE <- as.Date(meck_weather$DATE)
summary(meck_weather)
## DATE mean_precipation TAVG
## Min. :2021-01-04 Min. :0.00000 Min. :28.00
## 1st Qu.:2021-05-10 1st Qu.:0.00000 1st Qu.:48.00
## Median :2021-09-14 Median :0.00500 Median :62.00
## Mean :2021-09-14 Mean :0.11351 Mean :60.84
## 3rd Qu.:2022-01-18 3rd Qu.:0.09521 3rd Qu.:73.00
## Max. :2022-05-25 Max. :1.77937 Max. :84.00
colnames(meck_weather)[1]<-"Date"
summary(meck_weather)
## Date mean_precipation TAVG
## Min. :2021-01-04 Min. :0.00000 Min. :28.00
## 1st Qu.:2021-05-10 1st Qu.:0.00000 1st Qu.:48.00
## Median :2021-09-14 Median :0.00500 Median :62.00
## Mean :2021-09-14 Mean :0.11351 Mean :60.84
## 3rd Qu.:2022-01-18 3rd Qu.:0.09521 3rd Qu.:73.00
## Max. :2022-05-25 Max. :1.77937 Max. :84.00
#new hanover weather: data preprocessing#
hanover_weather<- read.csv("new_hanover_weather.csv")
glimpse(hanover_weather)
## Rows: 10,646
## Columns: 8
## $ STATION <chr> "USC00319461", "USC00319461", "USC00319461", "USC00319461", "U…
## $ NAME <chr> "WILMINGTON 7 SE, NC US", "WILMINGTON 7 SE, NC US", "WILMINGTO…
## $ DATE <chr> "2021-01-04", "2021-01-05", "2021-01-06", "2021-01-07", "2021-…
## $ PRCP <dbl> 0.00, 0.00, 0.04, 0.00, 0.66, 0.06, 0.00, 0.00, 0.26, 0.02, 0.…
## $ TAVG <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ TMAX <int> 68, 52, 52, 51, 51, 54, 50, 51, 55, 49, 55, 57, 61, 52, 52, 57…
## $ TMIN <int> 47, 36, 36, 32, 32, 37, 31, 31, 33, 38, 38, 36, 36, 32, 32, 31…
## $ TOBS <int> 47, 39, 36, 32, 43, 37, 32, 33, 45, 38, 42, 36, 41, 32, 42, 31…
sum(is.na(hanover_weather$PRCP))
## [1] 181
hanover_weather <-
hanover_weather%>% mutate(PRCP = replace_na(PRCP,mean(PRCP,na.rm=TRUE)))
hanover_weather_prcp <- hanover_weather %>% group_by(DATE) %>% summarise(mean_precipation = mean(PRCP))
hanover_weather_prcp
## # A tibble: 507 × 2
## DATE mean_precipation
## <chr> <dbl>
## 1 2021-01-04 0.0123
## 2 2021-01-05 0.0171
## 3 2021-01-06 0.084
## 4 2021-01-07 0
## 5 2021-01-08 0.708
## 6 2021-01-09 0.0533
## 7 2021-01-10 0.0106
## 8 2021-01-11 0.0393
## 9 2021-01-12 0.475
## 10 2021-01-13 0.0813
## # … with 497 more rows
sum(is.na(hanover_weather$TAVG)) #no data
## [1] 10646
sum(is.na(hanover_weather$TMIN))
## [1] 9222
#which(is.na(hanover_weather$TMIN))
sum(is.na(hanover_weather$TMAX))
## [1] 9221
#which(is.na(hanover_weather$TMAX))
full_temp_data_new_hanover <-
hanover_weather[complete.cases(hanover_weather$TMIN),]
full_temp_data_new_hanover
## STATION NAME DATE PRCP TAVG
## 1 USC00319461 WILMINGTON 7 SE, NC US 2021-01-04 0.00 NA
## 2 USC00319461 WILMINGTON 7 SE, NC US 2021-01-05 0.00 NA
## 3 USC00319461 WILMINGTON 7 SE, NC US 2021-01-06 0.04 NA
## 4 USC00319461 WILMINGTON 7 SE, NC US 2021-01-07 0.00 NA
## 5 USC00319461 WILMINGTON 7 SE, NC US 2021-01-08 0.66 NA
## 6 USC00319461 WILMINGTON 7 SE, NC US 2021-01-09 0.06 NA
## 7 USC00319461 WILMINGTON 7 SE, NC US 2021-01-10 0.00 NA
## 8 USC00319461 WILMINGTON 7 SE, NC US 2021-01-11 0.00 NA
## 9 USC00319461 WILMINGTON 7 SE, NC US 2021-01-12 0.26 NA
## 10 USC00319461 WILMINGTON 7 SE, NC US 2021-01-13 0.02 NA
## 11 USC00319461 WILMINGTON 7 SE, NC US 2021-01-14 0.20 NA
## 12 USC00319461 WILMINGTON 7 SE, NC US 2021-01-15 0.00 NA
## 13 USC00319461 WILMINGTON 7 SE, NC US 2021-01-16 0.26 NA
## 14 USC00319461 WILMINGTON 7 SE, NC US 2021-01-17 0.00 NA
## 15 USC00319461 WILMINGTON 7 SE, NC US 2021-01-18 0.00 NA
## 16 USC00319461 WILMINGTON 7 SE, NC US 2021-01-19 0.00 NA
## 17 USC00319461 WILMINGTON 7 SE, NC US 2021-01-20 0.00 NA
## 18 USC00319461 WILMINGTON 7 SE, NC US 2021-01-21 0.00 NA
## 19 USC00319461 WILMINGTON 7 SE, NC US 2021-01-22 0.00 NA
## 20 USC00319461 WILMINGTON 7 SE, NC US 2021-01-23 0.00 NA
## 21 USC00319461 WILMINGTON 7 SE, NC US 2021-01-24 0.00 NA
## 22 USC00319461 WILMINGTON 7 SE, NC US 2021-01-25 0.02 NA
## 23 USC00319461 WILMINGTON 7 SE, NC US 2021-01-26 0.00 NA
## 24 USC00319461 WILMINGTON 7 SE, NC US 2021-01-27 0.18 NA
## 25 USC00319461 WILMINGTON 7 SE, NC US 2021-01-28 0.30 NA
## 26 USC00319461 WILMINGTON 7 SE, NC US 2021-01-29 0.00 NA
## 27 USC00319461 WILMINGTON 7 SE, NC US 2021-01-30 0.00 NA
## 28 USC00319461 WILMINGTON 7 SE, NC US 2021-01-31 0.00 NA
## 29 USC00319461 WILMINGTON 7 SE, NC US 2021-02-01 1.62 NA
## 30 USC00319461 WILMINGTON 7 SE, NC US 2021-02-02 1.60 NA
## 31 USC00319461 WILMINGTON 7 SE, NC US 2021-02-03 0.00 NA
## 32 USC00319461 WILMINGTON 7 SE, NC US 2021-02-04 0.00 NA
## 33 USC00319461 WILMINGTON 7 SE, NC US 2021-02-05 0.00 NA
## 34 USC00319461 WILMINGTON 7 SE, NC US 2021-02-06 0.00 NA
## 35 USC00319461 WILMINGTON 7 SE, NC US 2021-02-07 1.32 NA
## 36 USC00319461 WILMINGTON 7 SE, NC US 2021-02-08 0.00 NA
## 37 USC00319461 WILMINGTON 7 SE, NC US 2021-02-09 0.00 NA
## 38 USC00319461 WILMINGTON 7 SE, NC US 2021-02-10 0.06 NA
## 39 USC00319461 WILMINGTON 7 SE, NC US 2021-02-11 0.10 NA
## 40 USC00319461 WILMINGTON 7 SE, NC US 2021-02-12 0.15 NA
## 41 USC00319461 WILMINGTON 7 SE, NC US 2021-02-13 1.10 NA
## 42 USC00319461 WILMINGTON 7 SE, NC US 2021-02-14 1.28 NA
## 43 USC00319461 WILMINGTON 7 SE, NC US 2021-02-15 1.10 NA
## 44 USC00319461 WILMINGTON 7 SE, NC US 2021-02-16 0.30 NA
## 45 USC00319461 WILMINGTON 7 SE, NC US 2021-02-17 0.00 NA
## 46 USC00319461 WILMINGTON 7 SE, NC US 2021-02-18 0.02 NA
## 47 USC00319461 WILMINGTON 7 SE, NC US 2021-02-19 1.12 NA
## 48 USC00319461 WILMINGTON 7 SE, NC US 2021-02-20 0.50 NA
## 49 USC00319461 WILMINGTON 7 SE, NC US 2021-02-21 0.00 NA
## 50 USC00319461 WILMINGTON 7 SE, NC US 2021-02-22 0.06 NA
## 51 USC00319461 WILMINGTON 7 SE, NC US 2021-02-23 0.00 NA
## 52 USC00319461 WILMINGTON 7 SE, NC US 2021-02-24 0.00 NA
## 53 USC00319461 WILMINGTON 7 SE, NC US 2021-02-25 0.00 NA
## 54 USC00319461 WILMINGTON 7 SE, NC US 2021-02-26 0.00 NA
## 55 USC00319461 WILMINGTON 7 SE, NC US 2021-02-27 0.00 NA
## 56 USC00319461 WILMINGTON 7 SE, NC US 2021-02-28 0.00 NA
## 57 USC00319461 WILMINGTON 7 SE, NC US 2021-03-01 0.00 NA
## 58 USC00319461 WILMINGTON 7 SE, NC US 2021-03-02 0.00 NA
## 59 USC00319461 WILMINGTON 7 SE, NC US 2021-03-03 0.20 NA
## 60 USC00319461 WILMINGTON 7 SE, NC US 2021-03-04 0.41 NA
## 61 USC00319461 WILMINGTON 7 SE, NC US 2021-03-05 0.00 NA
## 62 USC00319461 WILMINGTON 7 SE, NC US 2021-03-06 0.00 NA
## 63 USC00319461 WILMINGTON 7 SE, NC US 2021-03-07 0.00 NA
## 64 USC00319461 WILMINGTON 7 SE, NC US 2021-03-08 0.00 NA
## 65 USC00319461 WILMINGTON 7 SE, NC US 2021-03-09 0.00 NA
## 66 USC00319461 WILMINGTON 7 SE, NC US 2021-03-10 0.00 NA
## 67 USC00319461 WILMINGTON 7 SE, NC US 2021-03-11 0.00 NA
## 68 USC00319461 WILMINGTON 7 SE, NC US 2021-03-12 0.00 NA
## 69 USC00319461 WILMINGTON 7 SE, NC US 2021-03-13 0.00 NA
## 70 USC00319461 WILMINGTON 7 SE, NC US 2021-03-14 0.00 NA
## 71 USC00319461 WILMINGTON 7 SE, NC US 2021-03-15 0.04 NA
## 72 USC00319461 WILMINGTON 7 SE, NC US 2021-03-16 0.02 NA
## 73 USC00319461 WILMINGTON 7 SE, NC US 2021-03-17 0.90 NA
## 74 USC00319461 WILMINGTON 7 SE, NC US 2021-03-18 0.00 NA
## 75 USC00319461 WILMINGTON 7 SE, NC US 2021-03-19 0.00 NA
## 76 USC00319461 WILMINGTON 7 SE, NC US 2021-03-20 0.00 NA
## 77 USC00319461 WILMINGTON 7 SE, NC US 2021-03-21 0.00 NA
## 78 USC00319461 WILMINGTON 7 SE, NC US 2021-03-22 0.00 NA
## 79 USC00319461 WILMINGTON 7 SE, NC US 2021-03-23 0.00 NA
## 80 USC00319461 WILMINGTON 7 SE, NC US 2021-03-24 0.10 NA
## 81 USC00319461 WILMINGTON 7 SE, NC US 2021-03-25 0.00 NA
## 82 USC00319461 WILMINGTON 7 SE, NC US 2021-03-26 0.00 NA
## 83 USC00319461 WILMINGTON 7 SE, NC US 2021-03-27 0.00 NA
## 84 USC00319461 WILMINGTON 7 SE, NC US 2021-03-28 0.00 NA
## 85 USC00319461 WILMINGTON 7 SE, NC US 2021-03-29 0.08 NA
## 86 USC00319461 WILMINGTON 7 SE, NC US 2021-03-30 0.00 NA
## 87 USC00319461 WILMINGTON 7 SE, NC US 2021-03-31 0.00 NA
## 88 USC00319461 WILMINGTON 7 SE, NC US 2021-04-01 0.80 NA
## 89 USC00319461 WILMINGTON 7 SE, NC US 2021-04-02 0.00 NA
## 90 USC00319461 WILMINGTON 7 SE, NC US 2021-04-03 0.00 NA
## 91 USC00319461 WILMINGTON 7 SE, NC US 2021-04-04 0.00 NA
## 92 USC00319461 WILMINGTON 7 SE, NC US 2021-04-05 0.00 NA
## 93 USC00319461 WILMINGTON 7 SE, NC US 2021-04-06 0.00 NA
## 94 USC00319461 WILMINGTON 7 SE, NC US 2021-04-07 0.00 NA
## 95 USC00319461 WILMINGTON 7 SE, NC US 2021-04-08 0.00 NA
## 96 USC00319461 WILMINGTON 7 SE, NC US 2021-04-09 0.00 NA
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## 7134 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-07 0.00 NA
## 7135 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-08 0.96 NA
## 7136 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-09 0.00 NA
## 7137 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-10 0.06 NA
## 7138 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-11 0.00 NA
## 7139 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-12 0.30 NA
## 7140 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-13 0.00 NA
## 7141 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-14 0.00 NA
## 7142 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-15 0.00 NA
## 7143 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-16 0.00 NA
## 7144 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-17 0.00 NA
## 7145 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-18 0.00 NA
## 7146 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-19 0.13 NA
## 7147 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-20 0.00 NA
## 7148 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-21 0.94 NA
## 7149 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-22 0.11 NA
## 7150 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-23 0.00 NA
## 7151 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-24 0.00 NA
## 7152 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-25 0.00 NA
## 7153 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-26 0.00 NA
## 7154 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-27 0.00 NA
## 7155 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-28 0.00 NA
## 7156 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-29 0.00 NA
## 7157 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-30 0.03 NA
## 7158 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2021-12-31 0.00 NA
## 7159 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-01 0.00 NA
## 7160 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-02 0.34 NA
## 7161 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-03 0.98 NA
## 7162 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-04 0.00 NA
## 7163 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-05 0.07 NA
## 7164 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-06 0.00 NA
## 7165 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-07 0.00 NA
## 7166 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-08 0.00 NA
## 7167 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-09 0.00 NA
## 7168 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-10 0.21 NA
## 7169 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-11 0.00 NA
## 7170 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-12 0.00 NA
## 7171 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-13 0.00 NA
## 7172 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-14 0.00 NA
## 7173 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-15 0.00 NA
## 7174 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-16 2.06 NA
## 7175 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-17 0.00 NA
## 7176 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-18 0.00 NA
## 7177 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-19 0.00 NA
## 7178 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-20 0.09 NA
## 7179 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-21 0.15 NA
## 7180 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-22 0.14 NA
## 7181 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-23 0.00 NA
## 7182 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-24 0.00 NA
## 7183 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-25 0.02 NA
## 7184 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-26 0.00 NA
## 7185 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-27 0.00 NA
## 7186 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-28 0.03 NA
## 7187 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-29 0.05 NA
## 7188 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-30 0.00 NA
## 7189 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-01-31 0.00 NA
## 7190 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-01 0.00 NA
## 7191 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-02 0.01 NA
## 7192 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-03 0.02 NA
## 7193 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-04 0.34 NA
## 7194 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-05 0.07 NA
## 7195 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-06 0.00 NA
## 7196 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-07 0.26 NA
## 7197 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-08 0.00 NA
## 7198 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-09 0.00 NA
## 7199 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-10 0.00 NA
## 7200 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-11 0.00 NA
## 7201 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-12 0.00 NA
## 7202 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-13 0.05 NA
## 7203 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-14 0.00 NA
## 7204 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-15 0.00 NA
## 7205 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-16 0.00 NA
## 7206 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-17 0.07 NA
## 7207 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-18 0.14 NA
## 7208 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-19 0.00 NA
## 7209 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-20 0.00 NA
## 7210 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-21 0.06 NA
## 7211 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-22 0.00 NA
## 7212 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-23 0.00 NA
## 7213 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-24 0.00 NA
## 7214 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-25 0.00 NA
## 7215 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-26 0.00 NA
## 7216 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-27 0.35 NA
## 7217 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-02-28 0.00 NA
## 7218 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-01 0.00 NA
## 7219 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-02 0.00 NA
## 7220 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-03 0.00 NA
## 7221 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-04 0.00 NA
## 7222 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-05 0.00 NA
## 7223 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-06 0.00 NA
## 7224 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-07 0.00 NA
## 7225 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-08 0.00 NA
## 7226 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-09 0.28 NA
## 7227 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-10 0.03 NA
## 7228 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-11 0.05 NA
## 7229 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-12 0.22 NA
## 7230 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-13 0.00 NA
## 7231 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-14 0.00 NA
## 7232 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-15 0.00 NA
## 7233 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-16 0.11 NA
## 7234 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-17 0.00 NA
## 7235 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-18 0.00 NA
## 7236 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-19 0.00 NA
## 7237 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-20 0.00 NA
## 7238 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-21 0.00 NA
## 7239 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-22 0.00 NA
## 7240 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-23 0.04 NA
## 7241 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-24 1.41 NA
## 7242 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-25 0.14 NA
## 7243 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-26 0.00 NA
## 7244 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-27 0.00 NA
## 7245 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-28 0.00 NA
## 7246 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-29 0.00 NA
## 7247 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-30 0.02 NA
## 7248 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-03-31 0.13 NA
## 7249 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-01 0.00 NA
## 7250 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-02 0.00 NA
## 7251 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-03 0.00 NA
## 7252 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-04 0.00 NA
## 7253 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-05 1.03 NA
## 7254 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-06 0.53 NA
## 7255 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-07 0.04 NA
## 7256 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-08 0.00 NA
## 7257 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-09 0.00 NA
## 7258 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-10 0.00 NA
## 7259 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-11 0.00 NA
## 7260 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-12 0.00 NA
## 7261 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-13 0.00 NA
## 7262 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-14 0.00 NA
## 7263 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-15 0.00 NA
## 7264 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-16 0.37 NA
## 7265 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-17 0.00 NA
## 7266 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-18 1.20 NA
## 7267 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-19 0.00 NA
## 7268 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-20 0.00 NA
## 7269 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-21 0.00 NA
## 7270 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-22 0.00 NA
## 7271 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-23 0.00 NA
## 7272 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-24 0.00 NA
## 7273 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-25 0.00 NA
## 7274 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-26 0.10 NA
## 7275 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-27 0.00 NA
## 7276 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-28 0.00 NA
## 7277 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-29 0.00 NA
## 7278 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-04-30 0.00 NA
## 7279 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-01 0.00 NA
## 7280 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-02 0.00 NA
## 7281 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-03 0.00 NA
## 7282 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-04 0.00 NA
## 7283 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-05 0.03 NA
## 7284 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-06 0.00 NA
## 7285 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-07 0.00 NA
## 7286 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-08 0.00 NA
## 7287 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-09 0.00 NA
## 7288 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-10 0.00 NA
## 7289 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-11 0.00 NA
## 7290 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-12 0.21 NA
## 7291 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-13 0.12 NA
## 7292 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-14 0.00 NA
## 7293 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-15 0.00 NA
## 7294 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-16 0.31 NA
## 7295 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-17 0.02 NA
## 7296 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-18 0.00 NA
## 7297 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-19 0.00 NA
## 7298 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-20 0.00 NA
## 7299 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-21 0.00 NA
## 7300 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-22 0.02 NA
## 7301 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-23 0.00 NA
## 7302 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-24 0.00 NA
## 7303 USW00013748 WILMINGTON INTERNATIONAL AIRPORT, NC US 2022-05-25 0.00 NA
## TMAX TMIN TOBS
## 1 68 47 47
## 2 52 36 39
## 3 52 36 36
## 4 51 32 32
## 5 51 32 43
## 6 54 37 37
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## 8 51 31 33
## 9 55 33 45
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full_temp_data_new_hanover[238,]
## STATION NAME DATE PRCP TAVG TMAX TMIN TOBS
## 239 USC00319461 WILMINGTON 7 SE, NC US 2021-08-31 0 NA 94 74 76
full_temp_data_new_hanover[237,]
## STATION NAME DATE PRCP TAVG TMAX TMIN TOBS
## 237 USC00319461 WILMINGTON 7 SE, NC US 2021-08-29 0 NA 88 64 76
full_temp_data_new_hanover[239,]
## STATION NAME DATE PRCP TAVG TMAX TMIN TOBS
## 240 USC00319461 WILMINGTON 7 SE, NC US 2021-09-01 0.04 NA 90 76 79
full_temp_data_new_hanover <- full_temp_data_new_hanover %>%
rowwise() %>%
mutate(TMED = median(c(TMIN:TMAX)))
table(full_temp_data_new_hanover$STATION)
##
## USC00319461 USC00319467 USW00013748
## 505 412 507
hanover_temp <- full_temp_data_new_hanover %>% group_by(DATE) %>% summarise(mean_temp = mean(TMED))
hanover_weather <- merge(hanover_weather_prcp,hanover_temp, order.by=DATE)
hanover_weather$DATE <- as.Date(hanover_weather$DATE)
summary(hanover_weather)
## DATE mean_precipation mean_temp
## Min. :2021-01-04 Min. :0.00000 Min. :30.00
## 1st Qu.:2021-05-10 1st Qu.:0.00000 1st Qu.:51.25
## Median :2021-09-14 Median :0.01057 Median :62.50
## Mean :2021-09-14 Mean :0.15017 Mean :62.64
## 3rd Qu.:2022-01-18 3rd Qu.:0.10680 3rd Qu.:74.71
## Max. :2022-05-25 Max. :3.82208 Max. :85.83
colnames(hanover_weather)[1]<-"Date"
summary(hanover_weather)
## Date mean_precipation mean_temp
## Min. :2021-01-04 Min. :0.00000 Min. :30.00
## 1st Qu.:2021-05-10 1st Qu.:0.00000 1st Qu.:51.25
## Median :2021-09-14 Median :0.01057 Median :62.50
## Mean :2021-09-14 Mean :0.15017 Mean :62.64
## 3rd Qu.:2022-01-18 3rd Qu.:0.10680 3rd Qu.:74.71
## Max. :2022-05-25 Max. :3.82208 Max. :85.83
#precipation and temp plots#
wake_prep_plot <- wake_weather %>% ggplot(aes(Date,mean_precipation)) +
geom_line() + xlab("") + ylab("") + theme_bw(base_size = 14)
meck_prep_plot <- meck_weather %>% ggplot(aes(Date,mean_precipation)) +
geom_line() + xlab("") + ylab("") + theme_bw(base_size = 14)
hanover_prep_plot <- hanover_weather %>% ggplot(aes(Date,mean_precipation)) +
geom_line() + ylab("") + theme_bw(base_size = 14)
png(filename="precipitation.png", res = 500,units = "cm", width = 20, height = 10)
grid.arrange(wake_prep_plot,meck_prep_plot,hanover_prep_plot,
left = text_grob("Mean Precipitaion (in inches)", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
wake_temp_plot <- wake_weather %>% ggplot(aes(Date,TAVG)) +
geom_line() + xlab("") + ylab("") + theme_bw(base_size = 14)
meck_temp_plot <- meck_weather %>% ggplot(aes(Date,TAVG)) +
geom_line() + xlab("") + ylab("") + theme_bw(base_size = 14)
hanover_temp_plot <- hanover_weather %>% ggplot(aes(Date,mean_temp)) +
geom_line() + ylab("") + theme_bw(base_size = 14)
png(filename="temp.png", res = 500,units = "cm", width = 20, height = 10)
grid.arrange(wake_temp_plot,meck_temp_plot,hanover_temp_plot,
left = text_grob("Average Temperature (in °F)", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
#merge datasets
full_cases_wastewater_weather_data <- merge(full_cases_wastewater_data,
wake_weather, order.by=Date)
full_cases_wastewater_weather_data_meck <- merge(full_cases_wastewater_data_meck,
meck_weather, order.by=Date)
full_cases_wastewater_weather_data_hanover <- merge(full_cases_wastewater_data_hanover,
hanover_weather, order.by=Date)
#Correlations
png(filename="wake_correlations.png",
res = 700,units = "cm", width = 20, height = 10)
ggpairs(full_cases_wastewater_weather_data,
columns = 2:5,
columnLabels = c("New Cases","Viral Gene",
"Precipitation", "Temperature")) +
theme_bw()
dev.off()
## quartz_off_screen
## 2
png(filename="meck_correlations.png",
res = 700,units = "cm", width = 20, height = 10)
ggpairs(full_cases_wastewater_weather_data_meck,
columns = c(2,4:6),
columnLabels = c("New Cases","Viral Gene",
"Precipitation", "Temperature")) +
theme_bw()
dev.off()
## quartz_off_screen
## 2
png(filename="hanover_correlations.png",
res = 700,units = "cm", width = 20, height = 10)
ggpairs(full_cases_wastewater_weather_data_hanover,
columns = c(2:5),
columnLabels = c("New Cases","Viral Gene",
"Precipitation", "Temperature")) +
theme_bw()
dev.off()
## quartz_off_screen
## 2
Modelling COVID-19 cases only
ARIMA modelling
### Wake
df_wake_1 <- xts(df_wake$mean_new_cases,order.by = df_wake$Date)
df_wake_1 <- df_wake_1[-c(1,506,507,508),] #making even weekly data
attr(df_wake_1, 'frequency') <- 7
periodicity(df_wake_1)
## Daily periodicity from 2021-01-04 to 2022-05-22
df_wake_1_ts <- as.ts(df_wake_1)
plot(decompose(log(df_wake_1_ts))) #exponential growth is evident at the peakk
df_wake_seasonal_decomp <- decompose(log(df_wake_1_ts))
png(filename = "Additive_season.png",res = 700, units = "cm",width = 20, height = 14)
plot(df_wake_seasonal_decomp)
dev.off()
## quartz_off_screen
## 2
df_wake_deseasonal_decomp <- seasadj(df_wake_seasonal_decomp)
png(filename = "season_adjust.png",res = 700, units = "cm",width = 20, height = 12)
tsdisplay(df_wake_deseasonal_decomp, main = NULL)
dev.off()
## quartz_off_screen
## 2
#Forecasting
train_df_seasonal <- ts(log(df_wake_1_ts)[-c(491:504)], frequency=7)
test_df_seasonal <- log(df_wake_1_ts)[c(491:504)]
train_df1 <- df_wake_deseasonal_decomp[-c(491:504)]
test_df1 <- df_wake_deseasonal_decomp[c(491:504)]
lowest_rmse<-Inf
lowest_mae<-Inf
best_mod<-NULL
best_mod_mae<-NULL
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
rmse_mod_1 <- rmse(test_df1,forecast_fit$mean)
if (rmse_mod_1 < lowest_rmse){
lowest_rmse <- rmse_mod_1
best_mod <- arima_mod_1
}
}
} #arima(3,1,4) gives the lowest RMSE
lowest_rmse
## [1] 0.1988205
best_mod
## Series: train_df1
## ARIMA(3,1,4)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 ma4
## 1.6674 -1.3488 0.6348 -2.1967 2.1290 -1.2446 0.3569
## s.e. 0.1944 0.2716 0.1394 0.1979 0.3862 0.3110 0.1147
##
## sigma^2 = 0.1107: log likelihood = -152.62
## AIC=321.24 AICc=321.54 BIC=354.77
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
mae_mod <- mae(test_df1,forecast_fit$mean)
if (mae_mod < lowest_mae){
lowest_mae <- mae_mod
best_mod_mae <- arima_mod_1
}
}
} #arima(3,1,4) gives the lowest RMSE
best_mod_mae
## Series: train_df1
## ARIMA(3,1,4)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 ma4
## 1.6674 -1.3488 0.6348 -2.1967 2.1290 -1.2446 0.3569
## s.e. 0.1944 0.2716 0.1394 0.1979 0.3862 0.3110 0.1147
##
## sigma^2 = 0.1107: log likelihood = -152.62
## AIC=321.24 AICc=321.54 BIC=354.77
lowest_mae
## [1] 0.170638
wake_fit_1_arima <- Arima(train_df1, order = c(4,1,4))
coeftest(wake_fit_1_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.24418 0.34159 -0.7148 0.474722
## ar2 0.27374 0.12972 2.1103 0.034835 *
## ar3 -0.53331 0.20916 -2.5498 0.010779 *
## ar4 -0.16937 0.13204 -1.2827 0.199593
## ma1 -0.23533 0.34260 -0.6869 0.492137
## ma2 -0.51443 0.18590 -2.7673 0.005653 **
## ma3 0.61676 0.25956 2.3762 0.017491 *
## ma4 -0.03240 0.22251 -0.1456 0.884229
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
wake_fit_1_arima_forecast <- forecast::forecast(wake_fit_1_arima,h=14)
rmse(test_df1,wake_fit_1_arima_forecast$mean)
## [1] 0.2931432
mae(test_df1,wake_fit_1_arima_forecast$mean)
## [1] 0.2698372
checkresiduals(wake_fit_1_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(4,1,4)
## Q* = 13.984, df = 3, p-value = 0.002928
##
## Model df: 8. Total lags used: 11
exp(wake_fit_1_arima_forecast$mean[1])
## [1] 5.387371
exp(wake_fit_1_arima_forecast$lower[1,])
## 80% 95%
## 3.500936 2.786701
exp(wake_fit_1_arima_forecast$upper[1,])
## 80% 95%
## 8.290289 10.415101
exp(wake_fit_1_arima_forecast$mean[1])-exp(test_df1[1])
## [1] -3.330173
exp(test_df1[7])
## [1] 6.998252
exp(wake_fit_1_arima_forecast$mean[7])
## [1] 5.625453
exp(wake_fit_1_arima_forecast$lower[7,])
## 80% 95%
## 2.916609 2.059968
exp(wake_fit_1_arima_forecast$upper[7,])
## 80% 95%
## 10.85018 15.36224
exp(wake_fit_1_arima_forecast$mean[7])-exp(test_df1[7])
## [1] -1.372799
exp(wake_fit_1_arima_forecast$mean[14])
## [1] 5.625412
exp(wake_fit_1_arima_forecast$lower[14,])
## 80% 95%
## 2.349705 1.480158
exp(wake_fit_1_arima_forecast$upper[14,])
## 80% 95%
## 13.46776 21.37965
exp(wake_fit_1_arima_forecast$mean[14])-exp(test_df1[14])
## [1] -0.0813081
wake_fit_2_arima <- Arima(train_df1, order = c(3,1,4))
coeftest(wake_fit_2_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 1.66735 0.19440 8.5771 < 2.2e-16 ***
## ar2 -1.34881 0.27158 -4.9666 6.814e-07 ***
## ar3 0.63482 0.13938 4.5548 5.244e-06 ***
## ma1 -2.19667 0.19786 -11.1023 < 2.2e-16 ***
## ma2 2.12902 0.38619 5.5129 3.529e-08 ***
## ma3 -1.24457 0.31102 -4.0016 6.291e-05 ***
## ma4 0.35688 0.11466 3.1126 0.001855 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
wake_fit_2_arima_forecast <- forecast::forecast(wake_fit_2_arima ,h=14)
rmse(test_df1,wake_fit_2_arima_forecast$mean)
## [1] 0.1988205
mae(test_df1,wake_fit_2_arima_forecast$mean)
## [1] 0.170638
checkresiduals(wake_fit_2_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,4)
## Q* = 6.5951, df = 3, p-value = 0.08599
##
## Model df: 7. Total lags used: 10
wake_fit_3_arima <- Arima(train_df1, order = c(3,1,1))
coeftest(wake_fit_3_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.053777 0.110265 -0.4877 0.62576
## ar2 -0.140588 0.062396 -2.2532 0.02425 *
## ar3 -0.121527 0.054762 -2.2192 0.02647 *
## ma1 -0.415730 0.103846 -4.0033 6.246e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
wake_fit_3_arima_forecast <- forecast::forecast(wake_fit_3_arima,h=14)
rmse(test_df1,wake_fit_3_arima_forecast$mean)
## [1] 0.3182116
mae(test_df1,wake_fit_3_arima_forecast$mean)
## [1] 0.298623
checkresiduals(wake_fit_3_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,1)
## Q* = 23.78, df = 6, p-value = 0.0005732
##
## Model df: 4. Total lags used: 10
wake_res_acf <- ggAcf(residuals(wake_fit_1_arima)) +
theme_bw(base_size = 15) + ggtitle("")
wake_qqplot <- data.frame(y=residuals(wake_fit_1_arima)) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
png(filename = "arima_res_wake.png", res = 700,
units = "cm",width = 20, height = 10)
grid.arrange(wake_res_acf,wake_qqplot, ncol=2)
dev.off()
## quartz_off_screen
## 2
### Mecklenburg
mecklenburg_reported_cases <- subset(reported_cases,County=="Mecklenburg")
summary(mecklenburg_reported_cases)
## Index wwtp County Date
## Length:1375 Length:1375 Length:1375 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-06-16
## Mode :character Mode :character Mode :character Median :2021-10-08
## Mean :2021-10-02
## 3rd Qu.:2022-01-31
## Max. :2022-05-25
##
## population new_cases_per_10k
## Min. : 68685 Min. : 0.110
## 1st Qu.: 68685 1st Qu.: 0.990
## Median :120000 Median : 2.040
## Mean :124133 Mean : 3.982
## 3rd Qu.:182501 3rd Qu.: 4.330
## Max. :182501 Max. :47.580
## NA's :10
mecklenburg_reported_cases$new_cases_per_10k <-
LOCF(mecklenburg_reported_cases$new_cases_per_10k)
df_mecklenburg <- mecklenburg_reported_cases %>%
group_by(Date) %>%
summarise(mean_new_cases = mean(new_cases_per_10k))
df_mecklenburg_1 <- xts(df_mecklenburg$mean_new_cases,order.by = df_mecklenburg$Date)
df_mecklenburg_1 <- df_mecklenburg_1[-c(1,506,507,508),] #making even weekly data
attr(df_mecklenburg_1, 'frequency') <- 7
periodicity(df_mecklenburg_1)
## Daily periodicity from 2021-01-04 to 2022-05-22
df_mecklenburg_1_ts <- as.ts(df_mecklenburg_1)
seasonal_decomp_mecklenburg<- decompose(log(df_mecklenburg_1_ts))
deseasonal_decomp_mecklen <- seasadj(seasonal_decomp_mecklenburg)
#Forecasting
train_df_seasonal_mecklen <- ts(log(df_mecklenburg_1_ts)[-c(491:504)], frequency=7)
test_df_seasonal_mecklen <- log(df_mecklenburg_1_ts)[c(491:504)]
train_df1_mecklen <- deseasonal_decomp_mecklen[-c(491:504)]
test_df1_mecklen <- deseasonal_decomp_mecklen[c(491:504)]
lowest_rmse_meck<-Inf
best_mod_meck<-NULL
lowest_mae_meck<-Inf
best_mod_meck_mae<-NULL
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1_mecklen, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
rmse_mod_1 <- rmse(test_df1_mecklen,forecast_fit$mean)
if (rmse_mod_1 < lowest_rmse_meck){
lowest_rmse_meck <- rmse_mod_1
best_mod_meck <- arima_mod_1
}
}
} #arima(3,1,1) gives the lowest RMSE
best_mod_meck
## Series: train_df1_mecklen
## ARIMA(3,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## -0.0472 -0.1851 -0.0397 -0.4183
## s.e. 0.1330 0.0698 0.0635 0.1261
##
## sigma^2 = 0.1002: log likelihood = -129.59
## AIC=269.18 AICc=269.3 BIC=290.14
lowest_rmse_meck
## [1] 0.1169349
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1_mecklen, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
mae_mod <- mae(test_df1_mecklen,forecast_fit$mean)
if (mae_mod < lowest_mae_meck){
lowest_mae_meck <- mae_mod
best_mod_meck_mae <- arima_mod_1
}
}
} #arima(3,1,1) gives the lowest mae
best_mod_meck_mae
## Series: train_df1_mecklen
## ARIMA(3,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## -0.0472 -0.1851 -0.0397 -0.4183
## s.e. 0.1330 0.0698 0.0635 0.1261
##
## sigma^2 = 0.1002: log likelihood = -129.59
## AIC=269.18 AICc=269.3 BIC=290.14
lowest_mae_meck
## [1] 0.1015061
meck_mod_1_arima <- Arima(train_df1_mecklen, order = c(4,1,4))
coeftest(meck_mod_1_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.179200 2.855669 0.0628 0.9500
## ar2 0.571532 1.826062 0.3130 0.7543
## ar3 0.183666 1.138179 0.1614 0.8718
## ar4 -0.061576 0.292521 -0.2105 0.8333
## ma1 -0.712064 2.857448 -0.2492 0.8032
## ma2 -0.668450 3.339767 -0.2001 0.8414
## ma3 0.228473 0.841678 0.2714 0.7860
## ma4 0.276417 1.369902 0.2018 0.8401
meck_mod_1_arima_forecast <- forecast::forecast(meck_mod_1_arima , h=14)
rmse(test_df1_mecklen,meck_mod_1_arima_forecast$mean)
## [1] 0.2734803
mae(test_df1_mecklen,meck_mod_1_arima_forecast$mean)
## [1] 0.2377482
checkresiduals(meck_mod_1_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(4,1,4)
## Q* = 7.3206, df = 3, p-value = 0.06235
##
## Model df: 8. Total lags used: 11
exp(meck_mod_1_arima_forecast$mean[1])
## [1] 3.671556
exp(meck_mod_1_arima_forecast$lower[1,])
## 80% 95%
## 2.478145 2.012571
exp(meck_mod_1_arima_forecast$upper[1,])
## 80% 95%
## 5.439683 6.698061
exp(meck_mod_1_arima_forecast$mean[1])- exp(test_df1_mecklen[1])
## [1] 0.6454289
exp(meck_mod_1_arima_forecast$mean[7])
## [1] 4.497959
exp(meck_mod_1_arima_forecast$lower[7,])
## 80% 95%
## 2.606630 1.952778
exp(meck_mod_1_arima_forecast$upper[7,])
## 80% 95%
## 7.761607 10.360438
exp(meck_mod_1_arima_forecast$mean[7])-exp(test_df1_mecklen[7])
## [1] 0.643501
exp(meck_mod_1_arima_forecast$mean[14])
## [1] 5.36376
exp(meck_mod_1_arima_forecast$lower[14,])
## 80% 95%
## 2.371565 1.539604
exp(meck_mod_1_arima_forecast$upper[14,])
## 80% 95%
## 12.13120 18.68658
exp(meck_mod_1_arima_forecast$mean[14])-exp(test_df1_mecklen[14])
## [1] 2.34382
meck_mod_2_arima <- Arima(train_df1_mecklen, order = c(3,1,4))
coeftest(meck_mod_2_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.913670 2.674093 0.3417 0.7326
## ar2 0.070303 2.548185 0.0276 0.9780
## ar3 -0.050111 0.183544 -0.2730 0.7848
## ma1 -1.446301 2.676266 -0.5404 0.5889
## ma2 0.221491 3.956001 0.0560 0.9554
## ma3 0.333399 0.923784 0.3609 0.7182
## ma4 -0.043563 0.592916 -0.0735 0.9414
meck_mod_2_arima_forecast <- forecast::forecast(meck_mod_2_arima , h=14)
rmse(test_df1_mecklen,meck_mod_2_arima_forecast$mean)
## [1] 0.2746343
mae(test_df1_mecklen,meck_mod_2_arima_forecast$mean)
## [1] 0.2388543
checkresiduals(meck_mod_2_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,4)
## Q* = 3.8301, df = 3, p-value = 0.2804
##
## Model df: 7. Total lags used: 10
meck_mod_3_arima <- Arima(train_df1_mecklen, order = c(3,1,1))
coeftest(meck_mod_3_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.047185 0.133005 -0.3548 0.7227680
## ar2 -0.185127 0.069811 -2.6518 0.0080054 **
## ar3 -0.039679 0.063536 -0.6245 0.5322946
## ma1 -0.418331 0.126070 -3.3182 0.0009059 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
meck_mod_3_arima_forecast <- forecast::forecast(meck_mod_3_arima , h=14)
rmse(test_df1_mecklen,meck_mod_3_arima_forecast$mean)
## [1] 0.1169349
mae(test_df1_mecklen,meck_mod_3_arima_forecast$mean)
## [1] 0.1015061
checkresiduals(meck_mod_3_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,1)
## Q* = 27.175, df = 6, p-value = 0.0001343
##
## Model df: 4. Total lags used: 10
meck_res_acf <- ggAcf(residuals(meck_mod_1_arima)) +
theme_bw(base_size = 15) + ggtitle("")
meck_qqplot <- data.frame(y=residuals(meck_mod_1_arima)) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
png(filename = "arima_res_meck.png", res = 700,
units = "cm",width = 20, height = 10)
grid.arrange(meck_res_acf,meck_qqplot, ncol=2)
dev.off()
## quartz_off_screen
## 2
##New Hanover
new_hanover_reported_cases <- subset(reported_cases,County=="New Hanover")
summary(new_hanover_reported_cases)
## Index wwtp County Date
## Length:1011 Length:1011 Length:1011 Min. :2021-01-03
## Class :character Class :character Class :character 1st Qu.:2021-05-11
## Mode :character Mode :character Mode :character Median :2021-09-15
## Mean :2021-09-14
## 3rd Qu.:2022-01-19
## Max. :2022-05-25
##
## population new_cases_per_10k
## Min. :58361 Min. : 0.300
## 1st Qu.:58361 1st Qu.: 0.340
## Median :58361 Median : 1.710
## Mean :63029 Mean : 3.529
## 3rd Qu.:67743 3rd Qu.: 3.600
## Max. :67743 Max. :48.490
## NA's :37
new_hanover_reported_cases$new_cases_per_10k <-
LOCF(new_hanover_reported_cases$new_cases_per_10k)
df_new_hanover <- new_hanover_reported_cases %>%
group_by(Date) %>%
summarise(mean_new_cases = mean(new_cases_per_10k))
df_new_hanover_1 <-
xts(df_new_hanover$mean_new_cases,order.by = df_new_hanover$Date)
df_new_hanover_1 <- df_new_hanover_1[-c(1,506,507,508),] #making even weekly data
attr(df_new_hanover_1, 'frequency') <- 7
periodicity(df_new_hanover_1)
## Daily periodicity from 2021-01-04 to 2022-05-22
df_new_hanover_1_ts <- as.ts(df_new_hanover_1)
new_hanover_seasonal_decomp <- decompose(log(df_new_hanover_1_ts))
new_hanover_deseasonal_decomp <- seasadj(new_hanover_seasonal_decomp)
#forecasting
train_df_seasonal_new_hanover <- log(df_new_hanover_1_ts)[-c(491:504)]
test_df_seasonal_new_hanover <- log(df_new_hanover_1_ts)[c(491:504)]
train_df1_new_hanover<- new_hanover_deseasonal_decomp[-c(491:504)]
test_df1_new_hanover <- new_hanover_deseasonal_decomp[c(491:504)]
lowest_rmse_hanover<-Inf
best_mod_hanover<-NULL
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1_new_hanover, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
rmse_mod_1 <- rmse(test_df1_new_hanover,forecast_fit$mean)
if (rmse_mod_1 < lowest_rmse_hanover){
lowest_rmse_hanover <- rmse_mod_1
best_mod_hanover <- arima_mod_1
}
}
}
best_mod_hanover #arima(4,1,4), arima(3,1,3)
## Series: train_df1_new_hanover
## ARIMA(4,1,4)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2 ma3 ma4
## 0.6073 -0.5023 1.0178 -0.2324 -1.1493 0.6785 -1.2525 0.8249
## s.e. 0.0624 0.0370 0.0346 0.0599 0.0400 0.0242 0.0399 0.0420
##
## sigma^2 = 0.1368: log likelihood = -205.8
## AIC=429.6 AICc=429.98 BIC=467.33
lowest_rmse_hanover
## [1] 0.3371953
lowest_mae_hanover<-Inf
best_mod_hanover_mae<-NULL
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(train_df1_new_hanover, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
mae_mod_1 <- mae(test_df1_new_hanover,forecast_fit$mean)
if (mae_mod_1 < lowest_mae_hanover){
lowest_mae_hanover <- mae_mod_1
best_mod_hanover_mae <- arima_mod_1
}
}
}
best_mod_hanover_mae
## Series: train_df1_new_hanover
## ARIMA(4,1,4)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2 ma3 ma4
## 0.6073 -0.5023 1.0178 -0.2324 -1.1493 0.6785 -1.2525 0.8249
## s.e. 0.0624 0.0370 0.0346 0.0599 0.0400 0.0242 0.0399 0.0420
##
## sigma^2 = 0.1368: log likelihood = -205.8
## AIC=429.6 AICc=429.98 BIC=467.33
lowest_mae_hanover
## [1] 0.2450774
#since wake, meck have arima(4,1,4) as second best model out of the best models
#considered, arima(4,1,4) will be used for comparision, allows to accomodate complex data
new_hanover_mod_1_arima <- Arima(train_df1_new_hanover, order = c(3,1,1))
coeftest(new_hanover_mod_1_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.035479 0.100974 -0.3514 0.725309
## ar2 -0.133723 0.060751 -2.2012 0.027724 *
## ar3 -0.140904 0.054373 -2.5915 0.009557 **
## ma1 -0.463325 0.094406 -4.9078 9.211e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
new_hanover_mod_1_arima_forecast <- forecast::forecast(new_hanover_mod_1_arima , h=14)
rmse(test_df1_new_hanover,new_hanover_mod_1_arima_forecast$mean)
## [1] 0.3807585
mae(test_df1_new_hanover,new_hanover_mod_1_arima_forecast$mean)
## [1] 0.3233545
checkresiduals(new_hanover_mod_1_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,1)
## Q* = 30.235, df = 6, p-value = 3.546e-05
##
## Model df: 4. Total lags used: 10
new_hanover_mod_2_arima <- Arima(train_df1_new_hanover, order = c(3,1,4))
coeftest(new_hanover_mod_2_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.430642 0.267663 1.6089 0.1076
## ar2 0.138449 0.306255 0.4521 0.6512
## ar3 0.338331 0.450347 0.7513 0.4525
## ma1 -0.999079 0.241181 -4.1424 3.436e-05 ***
## ma2 -0.033418 0.291343 -0.1147 0.9087
## ma3 -0.284498 0.632338 -0.4499 0.6528
## ma4 0.404610 0.311841 1.2975 0.1945
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
new_hanover_mod_2_arima_forecast <- forecast::forecast(new_hanover_mod_2_arima , h=14)
rmse(test_df1_new_hanover,new_hanover_mod_2_arima_forecast$mean)
## [1] 0.3713594
mae(test_df1_new_hanover,new_hanover_mod_2_arima_forecast$mean)
## [1] 0.2635143
checkresiduals(new_hanover_mod_2_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,4)
## Q* = 9.1476, df = 3, p-value = 0.02739
##
## Model df: 7. Total lags used: 10
new_hanover_mod_3_arima <- Arima(train_df1_new_hanover, order = c(4,1,4))
coeftest(new_hanover_mod_3_arima)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.607271 0.062391 9.7333 < 2.2e-16 ***
## ar2 -0.502302 0.037004 -13.5743 < 2.2e-16 ***
## ar3 1.017773 0.034645 29.3775 < 2.2e-16 ***
## ar4 -0.232440 0.059887 -3.8813 0.0001039 ***
## ma1 -1.149288 0.040039 -28.7041 < 2.2e-16 ***
## ma2 0.678547 0.024190 28.0508 < 2.2e-16 ***
## ma3 -1.252469 0.039911 -31.3814 < 2.2e-16 ***
## ma4 0.824887 0.041974 19.6524 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
new_hanover_mod_3_arima_forecast <- forecast::forecast(new_hanover_mod_3_arima , h=14)
rmse(test_df1_new_hanover,new_hanover_mod_3_arima_forecast$mean)
## [1] 0.3371953
mae(test_df1_new_hanover,new_hanover_mod_3_arima_forecast$mean)
## [1] 0.2450774
checkresiduals(new_hanover_mod_3_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(4,1,4)
## Q* = 10.834, df = 3, p-value = 0.01266
##
## Model df: 8. Total lags used: 11
exp(new_hanover_mod_3_arima_forecast$mean[1])
## [1] 1.428806
exp(new_hanover_mod_3_arima_forecast$lower[1,])
## 80% 95%
## 0.8892070 0.6917811
exp(new_hanover_mod_3_arima_forecast$upper[1,])
## 80% 95%
## 2.295852 2.951060
exp(new_hanover_mod_3_arima_forecast$mean[1])-exp(test_df1_new_hanover[1])
## [1] 0.3205985
exp(new_hanover_mod_3_arima_forecast$mean[7])
## [1] 2.041789
exp(new_hanover_mod_3_arima_forecast$lower[7,])
## 80% 95%
## 1.0914095 0.7834069
exp(new_hanover_mod_3_arima_forecast$upper[7,])
## 80% 95%
## 3.819742 5.321505
exp(new_hanover_mod_3_arima_forecast$mean[7])-exp(test_df1_new_hanover[7])
## [1] -0.2166181
exp(new_hanover_mod_3_arima_forecast$mean[14])
## [1] 2.291011
exp(new_hanover_mod_3_arima_forecast$lower[14,])
## 80% 95%
## 0.9472997 0.5935452
exp(new_hanover_mod_3_arima_forecast$upper[14,])
## 80% 95%
## 5.540727 8.843016
exp(new_hanover_mod_3_arima_forecast$mean[14])-exp(test_df1_new_hanover[14])
## [1] 1.451784
hanover_res_acf <- ggAcf(residuals(new_hanover_mod_3_arima)) +
theme_bw(base_size = 15) + ggtitle("")
hanover_qqplot <- data.frame(y=residuals(new_hanover_mod_3_arima)) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
png(filename = "arima_res_hanover.png", res = 700,
units = "cm",width = 20, height = 10)
grid.arrange(hanover_res_acf,hanover_qqplot, ncol=2)
dev.off()
## quartz_off_screen
## 2
#forecasting plots
wake_forecast_plot <-
autoplot(wake_fit_1_arima_forecast) +
autolayer(wake_fit_1_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1,start = 491), series = "Observed") +
theme_bw() + ylab("") +
ggtitle(NULL) + theme(legend.position = "none") #wake
meck_forecast_plot <-
autoplot(meck_mod_1_arima_forecast) +
autolayer(meck_mod_1_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1_mecklen,start = 491), series = "Observed") +
theme_bw() + ylab("") +
ggtitle(NULL) + theme(legend.position = "none") #meck
hanover_forecast_plot <-
autoplot(new_hanover_mod_3_arima_forecast) +
autolayer(new_hanover_mod_3_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1_new_hanover,start = 491), series = "Observed") +
theme_bw() + ylab("")+
ggtitle(NULL) + theme(legend.position = "bottom")#new hanover
png(filename = "arima_forecasts.png",units = "cm",
res = 700, width = 20, height = 15)
grid.arrange(wake_forecast_plot, meck_forecast_plot,
hanover_forecast_plot,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
#forecasting ARIMA(3,1,1)
wake_forecast_plot_311 <- autoplot(wake_fit_3_arima_forecast) +
autolayer(wake_fit_3_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("")+
ggtitle(NULL) + theme(legend.position = "none") #wake
meck_forecast_plot_311 <- autoplot(meck_mod_3_arima_forecast) +
autolayer(meck_mod_3_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1_mecklen,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("")+
ggtitle(NULL) + theme(legend.position = "none") #meck
hanover_forecast_plot_311 <-
autoplot(new_hanover_mod_1_arima_forecast) +
autolayer(new_hanover_mod_1_arima_forecast, series = "Forecasted") +
autolayer(ts(test_df1_new_hanover,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("")+
ggtitle(NULL) + theme(legend.position = "bottom") #new hanover
SARIMA modelling
#Wake
best_sarima_mod <- NULL
lowest_sarima_mod_rmse <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
rmse_mod <- rmse(test_df_seasonal,forecast_fit$mean)
if (rmse_mod < lowest_sarima_mod_rmse){
lowest_sarima_mod_rmse <- rmse_mod
best_sarima_mod <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod
## Series: train_df_seasonal
## ARIMA(2,3,2)(1,1,2)[7]
##
## Coefficients:
## ar1 ar2 ma1 ma2 sar1 sma1 sma2
## -0.4003 -0.3414 -1.9616 0.9706 -0.9485 0.0086 -0.9719
## s.e. 0.0456 0.0167 0.0109 0.0115 0.0172 0.0168 0.0166
##
## sigma^2 = 0.1343: log likelihood = -200.33
lowest_sarima_mod_rmse
## [1] 0.1213027
best_sarima_mod_mae <- NULL
lowest_sarima_mod_mae <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
mae_mod <- mae(test_df_seasonal,forecast_fit$mean)
if (mae_mod < lowest_sarima_mod_mae){
lowest_sarima_mod_mae <- mae_mod
best_sarima_mod_mae <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod_mae
## Series: train_df_seasonal
## ARIMA(2,3,2)(1,1,2)[7]
##
## Coefficients:
## ar1 ar2 ma1 ma2 sar1 sma1 sma2
## -0.4003 -0.3414 -1.9616 0.9706 -0.9485 0.0086 -0.9719
## s.e. 0.0456 0.0167 0.0109 0.0115 0.0172 0.0168 0.0166
##
## sigma^2 = 0.1343: log likelihood = -200.33
lowest_sarima_mod_mae
## [1] 0.08304265
wake_sarima_mod_1 <- Arima(train_df_seasonal,
order = c(2,3,2),
seasonal =c(1,1,2),method="CSS")
wake_sarima_mod_1_forecast<- forecast::forecast(wake_sarima_mod_1, h=14)
rmse(test_df_seasonal,wake_sarima_mod_1_forecast$mean)
## [1] 0.1213027
mae(test_df_seasonal,wake_sarima_mod_1_forecast$mean)
## [1] 0.08304265
checkresiduals(wake_sarima_mod_1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)(1,1,2)[7]
## Q* = 54.244, df = 7, p-value = 2.105e-09
##
## Model df: 7. Total lags used: 14
exp(wake_sarima_mod_1_forecast$mean[1])
## [1] 3.259008
exp(wake_sarima_mod_1_forecast$lower[1,])
## 80% 95%
## 2.034780 1.585718
exp(wake_sarima_mod_1_forecast$upper[1,])
## 80% 95%
## 5.219792 6.697996
exp(wake_sarima_mod_1_forecast$mean[1])-exp(test_df_seasonal[1])
## [1] -1.155992
exp(wake_sarima_mod_1_forecast$mean[7])
## [1] 6.321962
exp(wake_sarima_mod_1_forecast$lower[7,])
## 80% 95%
## 2.480965 1.512080
exp(wake_sarima_mod_1_forecast$upper[7,])
## 80% 95%
## 16.10954 26.43194
exp(wake_sarima_mod_1_forecast$mean[7])-exp(test_df_seasonal[7])
## [1] 0.7769618
exp(wake_sarima_mod_1_forecast$mean[14])
## [1] 5.723943
exp(wake_sarima_mod_1_forecast$lower[14,])
## 80% 95%
## 1.0481530 0.4267143
exp(wake_sarima_mod_1_forecast$upper[14,])
## 80% 95%
## 31.25834 76.78093
exp(wake_sarima_mod_1_forecast$mean[14])-exp(test_df_seasonal[14])
## [1] 1.202276
wake_sarima_mod_2 <- Arima(train_df_seasonal,
order = c(2,0,1),
seasonal =c(1,1,2),method="CSS")
wake_sarima_mod_2_forecast<- forecast::forecast(wake_sarima_mod_2, h=14)
rmse(test_df_seasonal,wake_sarima_mod_2_forecast$mean)
## [1] 0.3779045
mae(test_df_seasonal,wake_sarima_mod_2_forecast$mean)
## [1] 0.360243
checkresiduals(wake_sarima_mod_2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,0,1)(1,1,2)[7]
## Q* = 35.492, df = 8, p-value = 2.174e-05
##
## Model df: 6. Total lags used: 14
wake_sarima_mod_3 <- Arima(train_df_seasonal,
order = c(2,3,2),
seasonal =c(3,1,2),method="CSS")
wake_sarima_mod_3_forecast<- forecast::forecast(wake_sarima_mod_3, h=14)
rmse(test_df_seasonal,wake_sarima_mod_3_forecast$mean)
## [1] 0.5218837
mae(test_df_seasonal,wake_sarima_mod_3_forecast$mean)
## [1] 0.4289307
checkresiduals(wake_sarima_mod_3)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)(3,1,2)[7]
## Q* = 54.435, df = 5, p-value = 1.706e-10
##
## Model df: 9. Total lags used: 14
wake_res_acf_sarima <- ggAcf(residuals(wake_sarima_mod_1)) +
theme_bw(base_size = 15) + ggtitle("")
wake_qqplot_sarima <- data.frame(y=residuals(wake_sarima_mod_1)) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
grid.arrange(wake_res_acf_sarima ,wake_qqplot_sarima, ncol=2)
#Mecklenburg
best_sarima_mod_meck <- NULL
lowest_sarima_mod_meck_rmse <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal_mecklen, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
rmse_mod <- rmse(test_df_seasonal_mecklen,forecast_fit$mean)
if (rmse_mod < lowest_sarima_mod_meck_rmse){
lowest_sarima_mod_meck_rmse <- rmse_mod
best_sarima_mod_meck <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod_meck
## Series: train_df_seasonal_mecklen
## ARIMA(2,0,1)(1,1,2)[7]
##
## Coefficients:
## ar1 ar2 ma1 sar1 sma1 sma2
## 1.0915 -0.1004 -0.6035 0.2582 -1.1374 0.1774
## s.e. 0.0675 0.0666 0.0503 0.1416 0.1340 0.1290
##
## sigma^2 = 0.1026: log likelihood = -136.97
lowest_sarima_mod_meck_rmse
## [1] 0.09694679
best_sarima_mod_mae_meck <- NULL
lowest_sarima_mod_meck_mae <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal_mecklen, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
mae_mod <- mae(test_df_seasonal_mecklen,forecast_fit$mean)
if (mae_mod < lowest_sarima_mod_meck_mae){
lowest_sarima_mod_meck_mae <- mae_mod
best_sarima_mod_mae_meck <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod_mae_meck
## Series: train_df_seasonal_mecklen
## ARIMA(2,0,1)(1,1,1)[7]
##
## Coefficients:
## ar1 ar2 ma1 sar1 sma1
## 1.0838 -0.0939 -0.5950 0.0622 -0.9491
## s.e. 0.0672 0.0663 0.0503 0.0536 0.0227
##
## sigma^2 = 0.1026: log likelihood = -137.6
lowest_sarima_mod_meck_mae
## [1] 0.08221429
meck_sarima_mod_1 <- Arima(train_df_seasonal_mecklen,
order = c(2,3,2),
seasonal =c(1,1,2),method="CSS")
meck_sarima_mod_1_forecast <- forecast::forecast(meck_sarima_mod_1, h=14)
rmse(test_df_seasonal_mecklen,meck_sarima_mod_1_forecast$mean)
## [1] 0.1487362
mae(test_df_seasonal_mecklen,meck_sarima_mod_1_forecast$mean)
## [1] 0.1118273
checkresiduals(meck_sarima_mod_1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)(1,1,2)[7]
## Q* = 33.844, df = 7, p-value = 1.842e-05
##
## Model df: 7. Total lags used: 14
exp(meck_sarima_mod_1_forecast$mean[1])
## [1] 2.552191
exp(meck_sarima_mod_1_forecast$lower[1,])
## 80% 95%
## 1.670002 1.334165
exp(meck_sarima_mod_1_forecast$upper[1,])
## 80% 95%
## 3.900402 4.882215
exp(meck_sarima_mod_1_forecast$mean[1])-exp(test_df_seasonal_mecklen[1])
## [1] 0.4455245
exp(meck_sarima_mod_1_forecast$mean[7])
## [1] 2.634972
exp(meck_sarima_mod_1_forecast$lower[7,])
## 80% 95%
## 1.148288 0.739766
exp(meck_sarima_mod_1_forecast$upper[7,])
## 80% 95%
## 6.046460 9.385503
exp(meck_sarima_mod_1_forecast$mean[7])-exp(test_df_seasonal_mecklen[7])
## [1] -0.1516949
exp(meck_sarima_mod_1_forecast$mean[14])
## [1] 2.224326
exp(meck_sarima_mod_1_forecast$lower[14,])
## 80% 95%
## 0.5145110 0.2370394
exp(meck_sarima_mod_1_forecast$upper[14,])
## 80% 95%
## 9.61617 20.87259
exp(meck_sarima_mod_1_forecast$mean[14])-exp(test_df_seasonal_mecklen[14])
## [1] 0.0409925
meck_sarima_mod_2 <- Arima(train_df_seasonal_mecklen,
order = c(2,0,1),
seasonal =c(1,1,2),method="CSS")
meck_sarima_mod_2_forecast <- forecast::forecast(meck_sarima_mod_2, h=14)
rmse(test_df_seasonal_mecklen,meck_sarima_mod_2_forecast$mean)
## [1] 0.09694679
mae(test_df_seasonal_mecklen,meck_sarima_mod_2_forecast$mean)
## [1] 0.08353163
checkresiduals(meck_sarima_mod_2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,0,1)(1,1,2)[7]
## Q* = 50.493, df = 8, p-value = 3.286e-08
##
## Model df: 6. Total lags used: 14
meck_sarima_mod_3 <- Arima(train_df_seasonal_mecklen,
order = c(2,3,2),
seasonal =c(3,1,2),method="CSS")
meck_sarima_mod_3_forecast <- forecast::forecast(meck_sarima_mod_3, h=14)
rmse(test_df_seasonal_mecklen,meck_sarima_mod_3_forecast$mean)
## [1] 0.215006
mae(test_df_seasonal_mecklen,meck_sarima_mod_3_forecast$mean)
## [1] 0.181207
checkresiduals(meck_sarima_mod_3)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)(3,1,2)[7]
## Q* = 40.792, df = 5, p-value = 1.033e-07
##
## Model df: 9. Total lags used: 14
meck_res_acf_sarima <- ggAcf(residuals(meck_sarima_mod_1)) +
theme_bw(base_size = 15) + ggtitle("")
meck_qqplot_sarima <- data.frame(y=residuals(meck_sarima_mod_1 )) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
grid.arrange(meck_res_acf_sarima ,meck_qqplot_sarima, ncol=2)
#New Hanover
best_sarima_mod_hanover <- NULL
lowest_sarima_mod_hanover_rmse <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal_new_hanover, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
rmse_mod <- rmse(test_df_seasonal_new_hanover,forecast_fit$mean)
if (rmse_mod < lowest_sarima_mod_hanover_rmse){
lowest_sarima_mod_hanover_rmse <- rmse_mod
best_sarima_mod_hanover <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod_hanover
## Series: train_df_seasonal_new_hanover
## ARIMA(3,3,3)(2,1,3)[7]
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2
## -1.4066 -0.6461 -0.2114 -0.8613 -0.8627 0.8074 -0.9656 -0.5930
## s.e. 0.0562 0.0808 0.0514 0.0373 0.0575 0.0369 0.1182 0.1257
## sma1 sma2 sma3
## 0.1722 -0.1534 -0.4581
## s.e. 0.1238 0.1024 0.0990
##
## sigma^2 = 0.2335: log likelihood = -335.12
lowest_sarima_mod_hanover_rmse
## [1] 0.2774404
best_sarima_mod_mae_hanover <- NULL
lowest_sarima_mod_hanover_mae <- Inf
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(train_df_seasonal_new_hanover, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
mae_mod <- mae(test_df_seasonal_new_hanover,forecast_fit$mean)
if (mae_mod < lowest_sarima_mod_hanover_mae){
lowest_sarima_mod_hanover_mae <- mae_mod
best_sarima_mod_mae_hanover <- sarima_mod_1
}
}
}
}
}
}
}
best_sarima_mod_mae_hanover
## Series: train_df_seasonal_new_hanover
## ARIMA(2,3,2)(3,1,2)[7]
##
## Coefficients:
## ar1 ar2 ma1 ma2 sar1 sar2 sar3 sma1
## -0.494 -0.1715 -1.9631 0.9687 -0.7427 0.2262 0.1693 -0.1067
## s.e. 0.042 0.0455 0.0097 0.0102 0.0834 0.0608 0.0426 0.0863
## sma2
## -0.7766
## s.e. 0.0835
##
## sigma^2 = 0.175: log likelihood = -270.02
lowest_sarima_mod_hanover_mae
## [1] 0.2228928
hanover_sarima_mod_1 <- Arima(train_df_seasonal_new_hanover,
order = c(2,3,2),
seasonal =c(1,1,2),method="CSS")
hanover_sarima_mod_1_forecast <- forecast::forecast(hanover_sarima_mod_1, h=14)
rmse(test_df_seasonal_new_hanover,hanover_sarima_mod_1_forecast$mean)
## [1] 0.500865
mae(test_df_seasonal_new_hanover,hanover_sarima_mod_1_forecast$mean)
## [1] 0.3788101
checkresiduals(hanover_sarima_mod_1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)
## Q* = 152.08, df = 6, p-value < 2.2e-16
##
## Model df: 4. Total lags used: 10
exp(hanover_sarima_mod_1_forecast$mean[1])
## [1] 1.417873
exp(hanover_sarima_mod_1_forecast$lower[1,])
## 80% 95%
## 0.7340845 0.5180890
exp(hanover_sarima_mod_1_forecast$upper[1,])
## 80% 95%
## 2.738599 3.880344
exp(hanover_sarima_mod_1_forecast$mean[1])-exp(test_df1_new_hanover[1])
## [1] 0.309665
exp(hanover_sarima_mod_1_forecast$mean[7])
## [1] 1.869173
exp(hanover_sarima_mod_1_forecast$lower[7,])
## 80% 95%
## 0.3548533 0.1472504
exp(hanover_sarima_mod_1_forecast$upper[7,])
## 80% 95%
## 9.845783 23.726986
exp(hanover_sarima_mod_1_forecast$mean[7])-exp(test_df1_new_hanover[7])
## [1] -0.3892341
exp(hanover_sarima_mod_1_forecast$mean[14])
## [1] 2.142046
exp(hanover_sarima_mod_1_forecast$lower[14,])
## 80% 95%
## 0.13604701 0.03161997
exp(hanover_sarima_mod_1_forecast$upper[14,])
## 80% 95%
## 33.72628 145.10954
exp(hanover_sarima_mod_1_forecast$mean[14])-exp(test_df1_new_hanover[14])
## [1] 1.302819
hanover_sarima_mod_2 <- Arima(train_df_seasonal_new_hanover,
order = c(2,0,1),
seasonal =c(1,1,2),method="CSS")
hanover_sarima_mod_2_forecast <- forecast::forecast(hanover_sarima_mod_2, h=14)
rmse(test_df_seasonal_new_hanover,hanover_sarima_mod_2_forecast$mean)
## [1] 0.5744074
mae(test_df_seasonal_new_hanover,hanover_sarima_mod_2_forecast$mean)
## [1] 0.5232856
checkresiduals(hanover_sarima_mod_2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,0,1) with non-zero mean
## Q* = 110.61, df = 6, p-value < 2.2e-16
##
## Model df: 4. Total lags used: 10
hanover_sarima_mod_3 <- Arima(train_df_seasonal_new_hanover,
order = c(2,3,2),
seasonal =c(3,1,2),method="CSS")
hanover_sarima_mod_3_forecast <- forecast::forecast(hanover_sarima_mod_3, h=14)
rmse(test_df_seasonal_new_hanover,hanover_sarima_mod_3_forecast$mean)
## [1] 0.500865
mae(test_df_seasonal_new_hanover,hanover_sarima_mod_3_forecast$mean)
## [1] 0.3788101
checkresiduals(hanover_sarima_mod_3)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,3,2)
## Q* = 152.08, df = 6, p-value < 2.2e-16
##
## Model df: 4. Total lags used: 10
hanover_res_acf_sarima <- ggAcf(residuals(hanover_sarima_mod_1)) +
theme_bw(base_size = 15) + ggtitle("")
hanover_qqplot_sarima <- data.frame(y=residuals(hanover_sarima_mod_1)) %>%
ggplot(aes(sample=y)) + geom_qq() + geom_qq_line() +
theme_bw(base_size = 15) + ylab("Sample Quantiles") + xlab("Theoretical Quantiles")
grid.arrange(hanover_res_acf_sarima ,hanover_qqplot_sarima, ncol=2)
#Forecasting plots
wake_forecast_plot_sarima <- autoplot(wake_sarima_mod_1_forecast) +
autolayer(wake_sarima_mod_1_forecast, series = "Forecasted") +
autolayer(ts(test_df_seasonal,start = 71,frequency = 7), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
ggtitle(NULL) + theme(legend.position = "none") #wake
meck_forecast_plot_sarima <- autoplot(meck_sarima_mod_1_forecast) +
autolayer(meck_sarima_mod_1_forecast, series = "Forecasted") +
autolayer(ts(test_df_seasonal_mecklen,start = 71,frequency = 7), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
ggtitle(NULL) + theme(legend.position = "none") #meck
hanover_forecast_plot_sarima <-
autoplot(hanover_sarima_mod_1_forecast) +
autolayer(hanover_sarima_mod_1_forecast, series = "Forecasted") +
autolayer(ts(test_df_seasonal_new_hanover,start = 71,frequency = 7), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
ggtitle(NULL) + theme(legend.position = "bottom") #new hanover
png(filename = "sarima_forecasts.png",units = "cm",
res = 700, width = 20, height = 15)
grid.arrange(wake_forecast_plot_sarima, meck_forecast_plot_sarima,
hanover_forecast_plot_sarima,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
Incorporating wastewater and weather information
ARIMAX modelling- wastewater information only
#wake#
cases <- xts(full_cases_wastewater_weather_data$mean_new_cases,
order.by = full_cases_wastewater_data$Date)
attr(cases , 'frequency') <- 7
cases <- cases[-c(505,506,507)]
cases <- as.ts(cases)
cases_decompose <- decompose(log(cases))
cases_deseasonalise <- seasadj(cases_decompose)
viral_gene <- xts(full_cases_wastewater_weather_data$full_viral_gene_copies_per_person,
order.by = full_cases_wastewater_data$Date)
attr(viral_gene , 'frequency') <- 7
viral_gene <- viral_gene[-c(505,506,507)]
viral_gene <- as.ts(viral_gene)
viral_decompose <- decompose(log(viral_gene))
viral_deseasonalise <- seasadj(viral_decompose)
cases_train <- cases_deseasonalise[-c(491:504)]
cases_test <- cases_deseasonalise[c(491:504)]
viral_train <- viral_deseasonalise[-c(491:504)]
viral_test <- viral_deseasonalise[c(491:504)]
wastewater_mod_1_wake <- Arima(cases_train ,order = c(3,1,1),
xreg = viral_train)
coeftest(wastewater_mod_1_wake) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.047442 0.109886 -0.4317 0.66593
## ar2 -0.139566 0.062292 -2.2405 0.02506 *
## ar3 -0.120544 0.054927 -2.1946 0.02819 *
## ma1 -0.424449 0.103710 -4.0926 4.265e-05 ***
## xreg 0.016504 0.023024 0.7168 0.47349
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_wake <- forecast::forecast(wastewater_mod_1_wake, h=14,
xreg = viral_test)
rmse(cases_test,forecast_mod_1_wake$mean) #0.31
## [1] 0.31084
mae(cases_test,forecast_mod_1_wake$mean) #0.29
## [1] 0.2905952
checkresiduals(wastewater_mod_1_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 22.404, df = 5, p-value = 0.0004386
##
## Model df: 5. Total lags used: 10
wastewater_mod_2_wake <- Arima(cases_train ,order = c(4,1,4),
xreg = viral_train)
coeftest(wastewater_mod_2_wake) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.214677 0.362355 -0.5924 0.553549
## ar2 0.273832 0.122021 2.2441 0.024824 *
## ar3 -0.551651 0.213174 -2.5878 0.009659 **
## ar4 -0.158971 0.139375 -1.1406 0.254038
## ma1 -0.266203 0.363780 -0.7318 0.464311
## ma2 -0.501328 0.184487 -2.7174 0.006579 **
## ma3 0.640330 0.274584 2.3320 0.019701 *
## ma4 -0.053557 0.232556 -0.2303 0.817861
## xreg 0.011573 0.022317 0.5186 0.604072
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_2_wake <- forecast::forecast(wastewater_mod_2_wake, h=14,
xreg = viral_test)
rmse(cases_test,forecast_mod_2_wake$mean)
## [1] 0.2878107
mae(cases_test,forecast_mod_2_wake$mean)
## [1] 0.2638574
checkresiduals(wastewater_mod_2_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 13.8, df = 3, p-value = 0.00319
##
## Model df: 9. Total lags used: 12
exp(forecast_mod_2_wake$mean[1])
## [1] 5.383733
exp(forecast_mod_2_wake$lower[1,])
## 80% 95%
## 3.497436 2.783436
exp(forecast_mod_2_wake$upper[1,])
## 80% 95%
## 8.287381 10.413238
exp(forecast_mod_2_wake$mean[1]) - exp(cases_test[1])
## [1] -3.333811
exp(forecast_mod_2_wake$mean[7])
## [1] 5.644255
exp(forecast_mod_2_wake$lower[7,])
## 80% 95%
## 2.929634 2.070394
exp(forecast_mod_2_wake$upper[7,])
## 80% 95%
## 10.87426 15.38722
exp(forecast_mod_2_wake$mean[7])-exp(cases_test[7])
## [1] -1.353998
exp(forecast_mod_2_wake$mean[14])
## [1] 5.6726
exp(forecast_mod_2_wake$lower[14,])
## 80% 95%
## 2.375574 1.498512
exp(forecast_mod_2_wake$upper[14,])
## 80% 95%
## 13.54552 21.47357
exp(forecast_mod_2_wake$mean[14])-exp(cases_test[14])
## [1] -0.03411993
#Mecklenburg#
glimpse(full_cases_wastewater_weather_data_meck)
## Rows: 507
## Columns: 6
## $ Date <date> 2021-01-04, 2021-01-05, 2021-01-06,…
## $ mean_new_cases <dbl> 5.550, 11.860, 8.345, 7.765, 8.730, …
## $ mean_viral_gene_copies_per_person <dbl> 48863073, 16458455, 28467455, NA, NA…
## $ full_viral_gene_copies_per_person <dbl> 48863073, 16458455, 28467455, 284674…
## $ mean_precipation <dbl> 0.0023076923, 0.0123076923, 0.019166…
## $ TAVG <int> 47, 45, 42, 39, 38, 39, 37, 39, 45, …
cases_meck <- xts(full_cases_wastewater_weather_data_meck$mean_new_cases,
order.by = full_cases_wastewater_data_meck$Date)
attr(cases_meck , 'frequency') <- 7
cases_meck <- cases_meck[-c(505,506,507)]
cases_meck <- as.ts(cases_meck)
cases_decompose_meck <- decompose(log(cases_meck))
cases_deseasonalise_meck <- seasadj(cases_decompose_meck)
viral_gene_meck <- xts(full_cases_wastewater_weather_data_meck$full_viral_gene_copies_per_person,
order.by = full_cases_wastewater_data_meck$Date)
attr(viral_gene_meck , 'frequency') <- 7
viral_gene_meck <- viral_gene_meck[-c(505,506,507)]
viral_gene_meck <- as.ts(viral_gene_meck)
viral_decompose_meck <- decompose(log(viral_gene_meck))
viral_deseasonalise_meck <- seasadj(viral_decompose_meck)
cases_train_meck <- cases_deseasonalise_meck[-c(491:504)]
cases_test_meck <- cases_deseasonalise_meck[c(491:504)]
viral_train_meck <- viral_deseasonalise_meck[-c(491:504)]
viral_test_meck <- viral_deseasonalise_meck[c(491:504)]
wastewater_mod_1_meck <- Arima(cases_train_meck,order = c(3,1,1),
xreg = viral_train_meck)
coeftest(wastewater_mod_1_meck ) #wastewater insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.057166 0.140431 -0.4071 0.683952
## ar2 -0.186898 0.071762 -2.6044 0.009203 **
## ar3 -0.036454 0.064648 -0.5639 0.572831
## ma1 -0.400150 0.134646 -2.9719 0.002960 **
## xreg -0.032820 0.031448 -1.0436 0.296662
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_meck <- forecast::forecast(wastewater_mod_1_meck, h=14,
xreg = viral_test_meck)
rmse(cases_test_meck,forecast_mod_1_meck$mean)
## [1] 0.113133
mae(cases_test_meck,forecast_mod_1_meck$mean)
## [1] 0.09810705
checkresiduals(wastewater_mod_1_meck) #wastewater improves forecast
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 29.438, df = 5, p-value = 1.902e-05
##
## Model df: 5. Total lags used: 10
wastewater_mod_2_meck <- Arima(cases_train_meck ,order = c(4,1,4),
xreg = viral_train_meck, method = "CSS")
coeftest(wastewater_mod_2_meck) #insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.171347 1.706150 0.1004 0.9200
## ar2 0.391647 2.200231 0.1780 0.8587
## ar3 0.434785 0.919334 0.4729 0.6363
## ar4 -0.134944 0.350314 -0.3852 0.7001
## ma1 -0.702922 1.712747 -0.4104 0.6815
## ma2 -0.478628 3.173802 -0.1508 0.8801
## ma3 -0.118355 1.840228 -0.0643 0.9487
## ma4 0.439516 0.336950 1.3044 0.1921
## xreg -0.036932 0.027152 -1.3602 0.1738
forecast_mod_2_meck <- forecast::forecast(wastewater_mod_2_meck, h=14,
xreg = viral_test_meck)
rmse(cases_test_meck,forecast_mod_2_meck$mean)
## [1] 0.293157
mae(cases_test_meck,forecast_mod_2_meck$mean)
## [1] 0.2584049
checkresiduals(wastewater_mod_2_meck) #wastewater does not improve forecast
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 8.8691, df = 3, p-value = 0.03108
##
## Model df: 9. Total lags used: 12
exp(forecast_mod_2_meck$mean[1])
## [1] 3.715387
exp(forecast_mod_2_meck$lower[1,])
## 80% 95%
## 2.510192 2.039657
exp(forecast_mod_2_meck$upper[1,])
## 80% 95%
## 5.499219 6.767852
exp(forecast_mod_2_meck$mean[1])-exp(cases_test_meck[1])
## [1] 0.6892594
exp(forecast_mod_2_meck$mean[7])
## [1] 4.55529
exp(forecast_mod_2_meck$lower[7,])
## 80% 95%
## 2.619779 1.954714
exp(forecast_mod_2_meck$upper[7,])
## 80% 95%
## 7.92077 10.61570
exp(forecast_mod_2_meck$mean[7])-exp(cases_test_meck[7])
## [1] 0.7008319
exp(forecast_mod_2_meck$mean[14])
## [1] 5.46859
exp(forecast_mod_2_meck$lower[14,])
## 80% 95%
## 2.365444 1.517898
exp(forecast_mod_2_meck$upper[14,])
## 80% 95%
## 12.64265 19.70190
exp(forecast_mod_2_meck$mean[14])-exp(cases_test_meck[14])
## [1] 2.448649
#new hanover#
glimpse(full_cases_wastewater_weather_data_hanover)
## Rows: 507
## Columns: 5
## $ Date <date> 2021-01-04, 2021-01-05, 2021-01-06,…
## $ mean_new_cases <dbl> 3.770, 9.420, 8.220, 7.200, 5.765, 5…
## $ full_viral_gene_copies_per_person <dbl> 5659256, 5659256, 5659256, 5659256, …
## $ mean_precipation <dbl> 0.012307692, 0.017142857, 0.08400000…
## $ mean_temp <dbl> 49.33333, 42.66667, 42.66667, 41.000…
cases_hanover <- xts(full_cases_wastewater_weather_data_hanover$mean_new_cases,
order.by = full_cases_wastewater_data_hanover$Date)
attr(cases_hanover , 'frequency') <- 7
cases_hanover <- cases_hanover[-c(505,506,507)]
cases_hanover <- as.ts(cases_hanover)
cases_decompose_hanover <- decompose(log(cases_hanover))
cases_deseasonalise_hanover <- seasadj(cases_decompose_hanover)
viral_gene_hanover <- xts(full_cases_wastewater_weather_data_hanover$full_viral_gene_copies_per_person,
order.by = full_cases_wastewater_data_hanover$Date)
attr(viral_gene_hanover , 'frequency') <- 7
viral_gene_hanover <- viral_gene_hanover[-c(505,506,507)]
viral_gene_hanover <- as.ts(viral_gene_hanover)
viral_decompose_hanover <- decompose(log(viral_gene_hanover))
viral_deseasonalise_hanover <- seasadj(viral_decompose_hanover)
cases_train_hanover <- cases_deseasonalise_hanover[-c(491:504)]
cases_test_hanover <- cases_deseasonalise_hanover[c(491:504)]
viral_train_hanover <- viral_deseasonalise_hanover[-c(491:504)]
viral_test_hanover <- viral_deseasonalise_hanover[c(491:504)]
wastewater_mod_1_hanover <- Arima(cases_train_hanover ,order = c(3,1,1),
xreg = viral_train_hanover)
coeftest(wastewater_mod_1_hanover) #wastewater insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.0021883 0.0926492 0.0236 0.98116
## ar2 -0.1218986 0.0578334 -2.1078 0.03505 *
## ar3 -0.1434527 0.0531366 -2.6997 0.00694 **
## ma1 -0.5062411 0.0847791 -5.9713 2.354e-09 ***
## xreg 0.0659619 0.0263188 2.5063 0.01220 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_hanover <- forecast::forecast(wastewater_mod_1_hanover, h=14,
xreg = viral_test_hanover)
rmse(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.3605596
mae(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.295442
checkresiduals(wastewater_mod_1_hanover) #not improve forecast
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 31.446, df = 5, p-value = 7.646e-06
##
## Model df: 5. Total lags used: 10
wastewater_mod_1_hanover <- Arima(cases_train_hanover ,order = c(4,1,4),
xreg = viral_train_hanover)
coeftest(wastewater_mod_1_hanover) #wastewater insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.602240 0.063301 9.5139 < 2.2e-16 ***
## ar2 -0.500627 0.038988 -12.8405 < 2.2e-16 ***
## ar3 1.014573 0.035938 28.2312 < 2.2e-16 ***
## ar4 -0.226315 0.059438 -3.8076 0.0001403 ***
## ma1 -1.145547 0.040934 -27.9850 < 2.2e-16 ***
## ma2 0.676182 0.026457 25.5582 < 2.2e-16 ***
## ma3 -1.249619 0.031691 -39.4310 < 2.2e-16 ***
## ma4 0.817413 0.039434 20.7286 < 2.2e-16 ***
## xreg 0.033476 0.023612 1.4178 0.1562578
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_hanover <- forecast::forecast(wastewater_mod_1_hanover, h=14,
xreg = viral_test_hanover)
rmse(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.3494999
mae(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.2473775
checkresiduals(wastewater_mod_1_hanover) #not improve forecast
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 17.245, df = 3, p-value = 0.0006294
##
## Model df: 9. Total lags used: 12
#arimax(4,1,4) plots with only wastewater information#
arimax_414_plot_wake <- autoplot(forecast_mod_2_wake) +
autolayer(forecast_mod_2_wake, series = "Forecasted") +
autolayer(ts(cases_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time") +
ggtitle(NULL) + theme(legend.position = "none") #wake
arimax_414_plot_meck <- autoplot(forecast_mod_2_meck) +
autolayer(forecast_mod_2_meck, series = "Forecasted") +
autolayer(ts(cases_test_meck,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time") +
ggtitle(NULL) + theme(legend.position = "none")
arimax_414_plot_hanover <- autoplot(forecast_mod_1_hanover) +
autolayer(forecast_mod_1_hanover, series = "Forecasted") +
autolayer(ts(cases_test_hanover,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time") +
ggtitle(NULL) + theme(legend.position = "bottom")
png(filename = "arimax414_plots.png", res = 700, units = "cm",
width = 20, height = 18)
grid.arrange(arimax_414_plot_wake,
arimax_414_plot_meck,
arimax_414_plot_hanover,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
ARIMAX modelling - wastewater and weather information
#wake#
precipation_wake <- xts(full_cases_wastewater_weather_data$mean_precipation,
order.by = full_cases_wastewater_weather_data$Date)
attr(precipation_wake,'frequency') <- 7
precipation_wake <- precipation_wake[-c(505,506,507)]
precipation_wake <- as.ts(precipation_wake)
temp_wake <- xts(full_cases_wastewater_weather_data$TAVG,
order.by = full_cases_wastewater_weather_data$Date)
attr(temp_wake,'frequency') <- 7
temp_wake <- temp_wake[-c(505,506,507)]
temp_wake <- as.ts(temp_wake)
precipation_wake_train <- ts(precipation_wake[-c(491:504)])
precipation_wake_test <- ts(precipation_wake[c(491:504)])
temp_wake_train <- ts(temp_wake[-c(491:504)])
temp_wake_test <- ts(temp_wake[c(491:504)])
vars_wake <- ts.union(viral_train,precipation_wake_train,
temp_wake_train)
vars_test_wake <- ts.union(viral_test,precipation_wake_test,
temp_wake_test)
wastewater_weather_mod_1_wake <- Arima(cases_train ,order = c(3,1,1),
xreg = vars_wake)
coeftest(wastewater_weather_mod_1_wake) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.04725429 0.10876295 -0.4345 0.66395
## ar2 -0.13669089 0.06187876 -2.2090 0.02717 *
## ar3 -0.12606682 0.05473052 -2.3034 0.02126 *
## ma1 -0.42295848 0.10276067 -4.1160 3.856e-05 ***
## viral_train 0.01789114 0.02310192 0.7744 0.43867
## precipation_wake_train -0.04699524 0.04599086 -1.0218 0.30686
## temp_wake_train -0.00039493 0.00237290 -0.1664 0.86782
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_wake <- forecast::forecast(wastewater_weather_mod_1_wake, h=14,
xreg = vars_test_wake)
rmse(cases_test,forecast_mod_1_wake$mean)
## [1] 0.3054778
mae(cases_test,forecast_mod_1_wake$mean)
## [1] 0.2848204
checkresiduals(wastewater_weather_mod_1_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 22.532, df = 3, p-value = 5.054e-05
##
## Model df: 7. Total lags used: 10
wastewater_weather_mod_2_wake <- Arima(cases_train ,order = c(4,1,4),
xreg = vars_wake)
coeftest(wastewater_weather_mod_2_wake) # insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.2758694 0.0662381 -4.1648 3.116e-05 ***
## ar2 0.6285461 0.0467118 13.4558 < 2.2e-16 ***
## ar3 0.7855470 0.0401564 19.5622 < 2.2e-16 ***
## ar4 -0.3033917 0.0630207 -4.8142 1.478e-06 ***
## ma1 -0.2314046 0.0446697 -5.1803 2.215e-07 ***
## ma2 -0.8874472 0.0303010 -29.2878 < 2.2e-16 ***
## ma3 -0.5332980 0.0277722 -19.2026 < 2.2e-16 ***
## ma4 0.8024096 0.0411428 19.5030 < 2.2e-16 ***
## viral_train -0.0019084 0.0216879 -0.0880 0.9299
## precipation_wake_train -0.0397074 0.0447221 -0.8879 0.3746
## temp_wake_train 0.0010651 0.0022755 0.4681 0.6397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_2_wake <- forecast::forecast(wastewater_weather_mod_2_wake, h=14,
xreg = vars_test_wake)
rmse(cases_test,forecast_mod_2_wake$mean)
## [1] 0.2082233
mae(cases_test,forecast_mod_2_wake$mean)
## [1] 0.1842068
checkresiduals(wastewater_weather_mod_2_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 14.074, df = 3, p-value = 0.002806
##
## Model df: 11. Total lags used: 14
exp(forecast_mod_2_wake$mean[1])
## [1] 5.554114
exp(forecast_mod_2_wake$lower[1,])
## 80% 95%
## 3.62983 2.89799
exp(forecast_mod_2_wake$upper[1,])
## 80% 95%
## 8.498521 10.644682
exp(forecast_mod_2_wake$mean[1])-exp(cases_test[1])
## [1] -3.16343
exp(forecast_mod_2_wake$mean[7])
## [1] 6.454832
exp(forecast_mod_2_wake$lower[7,])
## 80% 95%
## 3.547241 2.583795
exp(forecast_mod_2_wake$upper[7,])
## 80% 95%
## 11.74571 16.12545
exp(forecast_mod_2_wake$mean[7])-exp(cases_test[7])
## [1] -0.5434207
exp(forecast_mod_2_wake$mean[14])
## [1] 7.376171
exp(forecast_mod_2_wake$lower[14,])
## 80% 95%
## 3.111867 1.970646
exp(forecast_mod_2_wake$upper[14,])
## 80% 95%
## 17.48401 27.60917
exp(forecast_mod_2_wake$mean[14]) -exp(cases_test[14])
## [1] 1.669451
wake_forecast_arimax_weather_plot <- autoplot(forecast_mod_1_wake) +
autolayer(forecast_mod_1_wake, series = "Forecasted") +
autolayer(ts(cases_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
xlab("") + ggtitle(NULL) + theme(legend.position = "none")
#mecklenburg#
precipation_meck <- xts(full_cases_wastewater_weather_data_meck$mean_precipation,
order.by = full_cases_wastewater_weather_data_meck$Date)
attr(precipation_meck,'frequency') <- 7
precipation_meck <- precipation_meck[-c(505,506,507)]
precipation_meck <- as.ts(precipation_meck)
temp_meck <- xts(full_cases_wastewater_weather_data_meck$TAVG,
order.by = full_cases_wastewater_weather_data_meck$Date)
attr(temp_meck,'frequency') <- 7
temp_meck <- temp_meck[-c(505,506,507)]
temp_meck <- as.ts(temp_meck)
precipation_meck_train <- ts(precipation_meck[-c(491:504)])
precipation_meck_test <- ts(precipation_meck[c(491:504)])
temp_meck_train <- ts(temp_meck[-c(491:504)])
temp_meck_test <- ts(temp_meck[c(491:504)])
vars_meck <- ts.union(viral_train_meck,precipation_meck_train,
temp_meck_train)
vars_test_meck <- ts.union(viral_test_meck,precipation_meck_test,
temp_meck_test)
wastewater_weather_mod_1_meck <- Arima(cases_train_meck ,order = c(3,1,1),
xreg = vars_meck)
coeftest(wastewater_weather_mod_1_meck) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.0616022 0.1398544 -0.4405 0.659594
## ar2 -0.1854175 0.0721950 -2.5683 0.010220 *
## ar3 -0.0361904 0.0648499 -0.5581 0.576801
## ma1 -0.4016311 0.1339991 -2.9973 0.002724 **
## viral_train_meck -0.0268804 0.0316277 -0.8499 0.395381
## precipation_meck_train -0.0492122 0.0526277 -0.9351 0.349737
## temp_meck_train 0.0029893 0.0025311 1.1810 0.237591
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_meck <- forecast::forecast(wastewater_weather_mod_1_meck, h=14,
xreg = vars_test_meck)
rmse(cases_test_meck,forecast_mod_1_meck$mean)
## [1] 0.1111443
mae(cases_test_meck,forecast_mod_1_meck$mean)
## [1] 0.09782189
checkresiduals(wastewater_weather_mod_1_meck)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 30.7, df = 3, p-value = 9.832e-07
##
## Model df: 7. Total lags used: 10
wastewater_weather_mod_2_meck <- Arima(cases_train_meck ,order = c(4,1,4),
xreg = vars_meck, method = "CSS")
coeftest(wastewater_weather_mod_2_meck) # insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.2760518 0.2869270 0.9621 0.33600
## ar2 0.1826836 0.3856264 0.4737 0.63569
## ar3 0.5869433 0.3106909 1.8892 0.05887 .
## ar4 -0.1862630 0.1151955 -1.6169 0.10589
## ma1 -0.8198434 0.2867637 -2.8590 0.00425 **
## ma2 -0.1946741 0.5414328 -0.3596 0.71918
## ma3 -0.3750422 0.4990118 -0.7516 0.45231
## ma4 0.5311884 0.2227153 2.3851 0.01708 *
## viral_train_meck -0.0308471 0.0268236 -1.1500 0.25014
## precipation_meck_train -0.0502851 0.0506466 -0.9929 0.32078
## temp_meck_train 0.0037193 0.0022594 1.6461 0.09974 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_2_meck <- forecast::forecast(wastewater_weather_mod_2_meck, h=14,
xreg = vars_test_meck)
rmse(cases_test_meck,forecast_mod_2_meck$mean)
## [1] 0.3275134
mae(cases_test_meck,forecast_mod_2_meck$mean)
## [1] 0.2866063
checkresiduals(wastewater_weather_mod_2_meck)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 11.897, df = 3, p-value = 0.007745
##
## Model df: 11. Total lags used: 14
exp(forecast_mod_2_meck$mean[1])
## [1] 3.593441
exp(forecast_mod_2_meck$lower[1,])
## 80% 95%
## 2.429426 1.974729
exp(forecast_mod_2_meck$upper[1,])
## 80% 95%
## 5.315172 6.539032
exp(forecast_mod_2_meck$mean[1])-exp(cases_test_meck[1])
## [1] 0.5673137
exp(forecast_mod_2_meck$mean[7])
## [1] 4.669721
exp(forecast_mod_2_meck$lower[7,])
## 80% 95%
## 2.701036 2.021471
exp(forecast_mod_2_meck$upper[7,])
## 80% 95%
## 8.073307 10.787340
exp(forecast_mod_2_meck$mean[7])-exp(cases_test_meck[7])
## [1] 0.8152623
exp(forecast_mod_2_meck$mean[14])
## [1] 5.787151
exp(forecast_mod_2_meck$lower[14,])
## 80% 95%
## 2.516034 1.618894
exp(forecast_mod_2_meck$upper[14,])
## 80% 95%
## 13.31108 20.68765
exp(forecast_mod_2_meck$mean[14]) -exp(cases_test_meck[14])
## [1] 2.767211
meck_forecast_arimax_weather_plot <- autoplot(forecast_mod_1_meck) +
autolayer(forecast_mod_1_meck, series = "Forecasted") +
autolayer(ts(cases_test_meck,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
xlab("") + ggtitle(NULL) + theme(legend.position = "none") #wake
#new hanover#
precipation_hanover <- xts(full_cases_wastewater_weather_data_hanover$mean_precipation,
order.by = full_cases_wastewater_weather_data_hanover$Date)
attr(precipation_hanover,'frequency') <- 7
precipation_hanover <- precipation_hanover[-c(505,506,507)]
precipation_hanover <- as.ts(precipation_hanover)
precipation_hanover
## Time Series:
## Start = c(1, 1)
## End = c(72, 7)
## Frequency = 7
## [1] 0.0123076923 0.0171428571 0.0840000000 0.0000000000 0.7082352941
## [6] 0.0533333333 0.0105655160 0.0393333333 0.4750000000 0.0813333333
## [11] 0.1594444444 0.0328571429 0.1632804587 0.0000000000 0.0000000000
## [16] 0.0000000000 0.0000000000 0.0023076923 0.0075000000 0.0105655160
## [21] 0.0000000000 0.1166666667 0.2350000000 0.1732804587 0.5529411765
## [26] 0.0023076923 0.0000000000 0.2227891611 1.4224405160 0.1640000000
## [31] 0.0126032171 0.0000000000 0.0193333333 0.0958263680 1.0804762240
## [36] 0.0186666667 0.0192857143 0.0958823529 0.0729411765 0.1841176471
## [41] 0.9183333333 0.6694117647 1.1544444444 0.1858823529 0.0000000000
## [46] 0.0894444444 1.0938888889 0.5237500000 0.0000000000 0.0685714286
## [51] 0.1637500000 0.0120748754 0.0000000000 0.0078571429 0.0568750000
## [56] 0.0000000000 0.0132698837 0.0605882353 0.1488888889 0.1325000000
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0120748754
## [66] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0166032171
## [71] 0.0033333333 0.0633333333 0.7929411765 0.0013333333 0.0056250000
## [76] 0.0164285714 0.0587500000 0.0119365504 0.0147058824 0.1123529412
## [81] 0.0000000000 0.0073333333 0.0000000000 0.0332698837 0.1168750000
## [86] 0.0000000000 0.1184354652 0.7840000000 0.0000000000 0.0000000000
## [91] 0.0000000000 0.0000000000 0.0000000000 0.0105655160 0.0000000000
## [96] 0.0000000000 0.0326666667 0.4247058824 0.0012500000 0.0000000000
## [101] 0.0000000000 0.0221428571 0.1594444444 0.0105655160 0.0073333333
## [106] 0.0000000000 0.0012500000 0.0000000000 0.0000000000 0.0000000000
## [111] 0.0000000000 0.0577777778 0.0739365504 0.0000000000 0.0000000000
## [116] 0.0000000000 0.0000000000 0.0000000000 0.0120748754 0.0053333333
## [121] 0.0268750000 0.0130655160 0.0000000000 0.1276470588 0.6204524128
## [126] 0.0000000000 0.0023529412 0.0711111111 0.0755000000 0.2299499082
## [131] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [136] 0.0000000000 0.0005882353 0.0093915698 0.0000000000 0.0084524128
## [141] 0.0047619048 0.1691666667 0.0076840116 0.0000000000 0.0128571429
## [146] 0.0080499170 0.2470833333 0.0005882353 0.0088972766 0.1150000000
## [151] 0.5795619302 3.8220833333 0.9991666667 0.0040909091 0.3095238605
## [156] 0.0947368421 0.0199048256 0.2234782609 0.1947826087 0.3408695652
## [161] 1.1747826087 0.0240476480 0.1403855482 1.2856521739 0.0025000000
## [166] 0.0000000000 0.0010000000 0.6334368807 0.6560455764 0.0447826087
## [171] 0.3436363636 0.0000000000 0.5631619302 0.5033333333 0.0000000000
## [176] 0.0189569768 0.0483333333 0.0086363636 0.0426923077 0.1865018560
## [181] 0.8764285714 0.0000000000 0.0135238605 0.0000000000 0.1409523810
## [186] 0.2792307692 0.5126923077 0.2636000000 0.0104347826 0.0319619302
## [191] 0.1036000000 0.2428770107 0.0213636364 0.1100000000 0.0299567389
## [196] 0.1554166667 0.9557326252 1.5284249329 0.1317391304 0.0314285714
## [201] 0.1141270107 0.0000000000 0.0000000000 0.0371428571 0.2707540213
## [206] 0.3268864714 0.0475000000 0.0000000000 0.0363636364 0.0977272727
## [211] 0.4218864714 0.7177777778 3.3614285714 0.0456802949 0.2051851852
## [216] 0.9453846154 1.8272000000 0.0214286449 0.0079619302 0.0053846154
## [221] 0.0000000000 0.0065018560 0.0000000000 0.0085714286 0.2650000000
## [226] 0.2056000000 1.1503120088 0.0216666667 0.1466137920 1.9556000000
## [231] 0.3349603440 0.2927238605 0.0014814815 0.0635374377 0.0051851852
## [236] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [241] 0.1027258019 0.2346666667 0.0081481481 0.0107326252 0.0062610465
## [246] 0.0020000000 0.1492240095 0.6482758621 0.1356802949 0.3543016085
## [251] 0.0053846154 0.0038461538 0.0053846154 0.0000000000 0.0085185185
## [256] 0.0088000000 0.0316000000 0.0200000000 0.0076840116 0.1560806351
## [261] 1.6235714286 3.6689326985 2.7427891611 0.0157692308 0.0052000000
## [266] 0.0000000000 0.0050000000 0.0065018560 0.0067619302 0.0000000000
## [271] 0.0196153846 0.0137103440 0.0000000000 0.1402918792 0.0162500000
## [276] 0.0958906762 0.0865018560 0.5026923077 0.0763203753 0.1125000000
## [281] 0.0507143653 0.0074603440 0.0071619302 0.0000000000 0.0126557022
## [286] 0.0072727273 0.0040000000 0.0045833333 0.0008000000 0.0000000000
## [291] 0.0000000000 0.0000000000 0.0009523810 0.0005263158 0.0287729428
## [296] 0.2070370370 0.0012000000 0.0231385571 0.2380769231 0.0108695652
## [301] 0.0000000000 0.0000000000 0.0067619302 0.0000000000 0.0004347826
## [306] 0.0000000000 0.0432880122 0.4868000000 0.0133883274 0.0070436773
## [311] 0.0070436773 0.0060000000 0.2466314169 0.0086542720 0.0000000000
## [316] 0.0137729428 0.0000000000 0.0067619302 0.0000000000 0.0041666667
## [321] 0.0000000000 0.0076840116 0.0194331672 0.0583333333 0.0000000000
## [326] 0.0123356312 0.1458333333 0.0404308693 0.0036842105 0.0151346310
## [331] 0.0000000000 0.0076840116 0.0067619302 0.0000000000 0.0000000000
## [336] 0.0000000000 0.0000000000 0.0073499242 0.1236684539 0.8696000000
## [341] 0.0112103440 0.0678260870 0.3156107937 0.0195238372 0.0067619302
## [346] 0.0013043478 0.0004347826 0.0000000000 0.0000000000 0.0665217391
## [351] 0.2788605897 0.0988461538 0.9503703704 0.0125000000 0.0000000000
## [356] 0.0000000000 0.0000000000 0.0000000000 0.0067619302 0.0000000000
## [361] 0.0172000000 0.0164000000 0.0013043478 0.0340909091 0.9176557022
## [366] 0.0379619302 0.0112000000 0.0992307692 0.0012000000 0.0000000000
## [371] 0.0000000000 0.1475000000 0.0000000000 0.0140873547 0.0008333333
## [376] 0.0004347826 0.0000000000 0.3595238095 1.5307619302 0.0076840116
## [381] 0.0070436773 0.0140909091 0.2259090909 0.3220000000 0.0000000000
## [386] 0.0000000000 0.0167316596 0.0158658298 0.0000000000 0.0147165836
## [391] 0.0920000000 0.0546712625 0.0076840116 0.0000000000 0.0004545455
## [396] 0.0421739130 0.0788095483 0.4266666667 0.0080499170 0.0511619302
## [401] 0.2022710868 0.0009523810 0.0000000000 0.0076840116 0.0076840116
## [406] 0.0094736842 0.1019619302 0.0090022979 0.0000000000 0.0043478261
## [411] 0.2084615385 0.0636363636 0.0000000000 0.0065000000 0.0382194894
## [416] 0.0019047619 0.0000000000 0.0000000000 0.0000000000 0.0194444444
## [421] 0.3540909091 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [426] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.2931818182
## [431] 0.1382194894 0.0142857143 0.2900000000 0.2694444444 0.0088972766
## [436] 0.0000000000 0.0146867503 0.1452380952 0.0088972766 0.0000000000
## [441] 0.0084524128 0.0088972766 0.0084524128 0.0104524128 0.7125000000
## [446] 1.0853770107 0.0005882353 0.0169048256 0.0000000000 0.0000000000
## [451] 0.0179048256 0.0108695652 0.1765384615 0.0000000000 0.0022727273
## [456] 0.0000000000 0.1022294662 0.6380769231 0.4553846154 0.0204545455
## [461] 0.0000000000 0.0076840116 0.0000000000 0.0073499242 0.0000000000
## [466] 0.0000000000 0.0000000000 0.0359524128 0.2143064459 0.3132936773
## [471] 1.0430434783 0.0090022979 0.0000000000 0.0000000000 0.0000000000
## [476] 0.0084524128 0.0000000000 0.0203934024 0.0545833333 0.0076840116
## [481] 0.0000000000 0.0000000000 0.0000000000 0.0080499170 0.0000000000
## [486] 0.0000000000 0.0549603440 0.0013636364 0.0014285714 0.0000000000
## [491] 0.0085261074 0.0000000000 0.0080499170 0.0527272727 0.1811619302
## [496] 0.3216666667 0.2157142857 0.0244524128 0.6560869565 0.0084524128
## [501] 0.0105655160 0.0011111111 0.0000000000 0.0111204857
temp_hanover<- xts(full_cases_wastewater_weather_data_hanover$mean_temp,
order.by = full_cases_wastewater_weather_data_hanover$Date)
attr(temp_hanover,'frequency') <- 7
temp_hanover <- temp_hanover[-c(505,506,507)]
temp_hanover <- as.ts(temp_hanover)
temp_hanover
## Time Series:
## Start = c(1, 1)
## End = c(72, 7)
## Frequency = 7
## [1] 49.33333 42.66667 42.66667 41.00000 44.16667 43.50000 40.66667 41.66667
## [9] 43.16667 45.83333 47.83333 47.66667 46.00000 40.83333 43.66667 44.00000
## [17] 46.16667 44.66667 47.66667 44.50000 41.50000 47.16667 58.16667 56.83333
## [25] 41.16667 37.66667 34.66667 47.83333 45.66667 41.16667 41.00000 39.50000
## [33] 48.16667 44.16667 42.66667 41.83333 50.16667 54.33333 52.50000 46.50000
## [41] 44.50000 40.33333 45.16667 56.83333 46.50000 43.33333 38.66667 37.33333
## [49] 37.83333 47.16667 55.83333 53.66667 59.00000 56.16667 60.50000 68.50000
## [57] 71.75000 57.50000 49.33333 52.33333 48.50000 44.16667 42.50000 43.33333
## [65] 50.00000 56.50000 57.16667 61.50000 61.50000 62.00000 57.83333 48.16667
## [73] 50.16667 61.50000 56.33333 47.50000 52.16667 57.50000 60.66667 65.00000
## [81] 66.50000 72.00000 70.83333 73.50000 59.50000 57.00000 66.50000 58.50000
## [89] 43.16667 41.83333 51.83333 61.00000 66.16667 70.33333 72.16667 70.50000
## [97] 70.33333 71.16667 69.83333 65.33333 62.50000 66.00000 59.50000 59.83333
## [105] 61.66667 62.50000 59.16667 64.83333 52.33333 50.66667 58.33333 62.33333
## [113] 61.00000 63.16667 68.66667 73.66667 71.16667 64.50000 63.50000 71.66667
## [121] 75.83333 77.00000 67.66667 60.33333 60.00000 66.16667 72.16667 66.33333
## [129] 58.33333 57.16667 59.83333 59.83333 62.16667 64.83333 68.33333 68.33333
## [137] 68.33333 66.83333 71.16667 76.83333 79.66667 78.66667 78.16667 84.25000
## [145] 84.00000 79.83333 66.50000 62.16667 66.33333 72.16667 75.16667 77.00000
## [153] 78.50000 78.25000 79.75000 82.25000 82.25000 81.00000 82.50000 81.25000
## [161] 76.25000 78.00000 79.75000 78.75000 77.50000 76.50000 80.00000 81.25000
## [169] 82.25000 80.00000 75.25000 70.50000 73.25000 77.50000 78.75000 79.50000
## [177] 80.25000 81.00000 81.83333 79.83333 76.66667 74.33333 75.50000 76.66667
## [185] 79.50000 80.66667 80.66667 81.33333 82.66667 83.83333 81.16667 81.16667
## [193] 81.66667 83.33333 81.83333 82.00000 78.16667 77.16667 79.83333 82.83333
## [201] 79.33333 75.66667 77.16667 80.00000 83.83333 79.16667 80.00000 83.66667
## [209] 85.83333 84.00000 80.50000 76.50000 73.75000 74.83333 75.00000 77.00000
## [217] 79.50000 78.16667 80.33333 83.16667 84.50000 83.16667 82.66667 82.33333
## [225] 81.50000 80.66667 81.83333 84.50000 81.50000 80.33333 80.25000 79.75000
## [233] 82.50000 82.25000 81.75000 81.00000 81.00000 80.25000 85.00000 83.50000
## [241] 82.00000 76.00000 71.50000 71.50000 72.33333 76.83333 79.16667 79.50000
## [249] 75.83333 71.50000 70.50000 71.50000 74.33333 75.83333 77.16667 78.50000
## [257] 80.66667 78.83333 77.33333 77.50000 76.66667 75.66667 68.16667 68.00000
## [265] 67.66667 68.33333 69.00000 71.66667 77.66667 74.66667 70.83333 69.33333
## [273] 70.50000 73.33333 75.50000 76.16667 74.66667 73.83333 73.50000 72.50000
## [281] 71.33333 69.66667 70.66667 71.33333 72.16667 72.33333 62.66667 58.83333
## [289] 59.83333 63.33333 67.66667 72.16667 67.66667 64.50000 69.50000 66.00000
## [297] 58.33333 59.33333 62.50000 59.66667 61.00000 60.00000 60.33333 56.83333
## [305] 53.16667 48.50000 52.16667 54.33333 54.83333 57.66667 59.33333 60.83333
## [313] 63.83333 58.50000 53.50000 51.50000 51.50000 57.66667 62.33333 55.66667
## [321] 48.50000 54.00000 57.25000 46.50000 40.00000 44.75000 48.75000 45.25000
## [329] 48.00000 49.25000 42.75000 49.83333 56.33333 60.83333 61.16667 59.33333
## [337] 62.66667 59.00000 48.33333 44.83333 52.83333 67.00000 56.00000 49.16667
## [345] 50.66667 52.83333 56.83333 63.83333 67.00000 59.83333 45.16667 43.83333
## [353] 47.33333 44.00000 45.66667 58.50000 64.16667 63.00000 66.66667 70.16667
## [361] 70.83333 69.83333 70.16667 69.33333 58.50000 42.66667 47.00000 51.00000
## [369] 47.50000 38.50000 48.50000 52.83333 37.33333 40.50000 43.50000 46.33333
## [377] 41.33333 45.00000 44.66667 41.16667 43.16667 51.00000 39.83333 30.00000
## [385] 31.50000 38.16667 42.16667 41.33333 36.66667 37.16667 35.50000 30.83333
## [393] 39.00000 42.33333 43.00000 56.83333 66.83333 51.66667 42.00000 44.00000
## [401] 43.66667 42.50000 48.16667 52.50000 55.33333 50.83333 41.50000 40.33333
## [409] 46.50000 57.33333 62.00000 50.83333 44.33333 51.00000 62.16667 69.00000
## [417] 63.00000 65.16667 59.25000 45.50000 47.00000 51.00000 55.50000 64.75000
## [425] 60.00000 57.25000 64.25000 72.00000 68.25000 62.50000 57.50000 51.00000
## [433] 55.75000 43.25000 41.75000 50.75000 59.50000 65.00000 62.50000 67.75000
## [441] 60.25000 53.50000 54.75000 62.50000 68.00000 61.75000 59.00000 54.00000
## [449] 50.00000 47.75000 53.25000 69.25000 65.83333 56.50000 58.66667 56.83333
## [457] 61.00000 70.50000 71.50000 61.00000 56.00000 52.66667 57.66667 69.16667
## [465] 70.16667 72.00000 64.50000 62.00000 65.33333 60.33333 54.00000 52.00000
## [473] 56.00000 63.33333 65.33333 67.50000 69.00000 72.16667 65.16667 59.16667
## [481] 59.00000 66.66667 71.33333 75.00000 78.00000 78.00000 76.00000 76.16667
## [489] 73.16667 60.00000 57.00000 61.00000 65.66667 68.16667 69.16667 69.16667
## [497] 72.50000 77.00000 74.75000 73.00000 79.00000 84.50000 84.25000 80.50000
precipation_hanover_train <- ts(precipation_hanover[-c(491:504)])
precipation_hanover_test <- ts(precipation_hanover[c(491:504)])
temp_hanover_train <- ts(temp_hanover[-c(491:504)])
temp_hanover_test <- ts(temp_hanover[c(491:504)])
vars_hanover <- ts.union(viral_train_hanover,precipation_hanover_train,
temp_hanover_train)
vars_test_hanover <- ts.union(viral_test_hanover,precipation_hanover_test,
temp_hanover_test)
wastewater_weather_mod_1_hanover <- Arima(cases_train_hanover ,order = c(3,1,1),
xreg = vars_hanover)
coeftest(wastewater_weather_mod_1_hanover) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.00333870 0.09302964 -0.0359 0.971371
## ar2 -0.12057485 0.05821491 -2.0712 0.038340 *
## ar3 -0.14248945 0.05319887 -2.6784 0.007397 **
## ma1 -0.50447808 0.08511124 -5.9273 3.08e-09 ***
## viral_train_hanover 0.06713847 0.02623437 2.5592 0.010492 *
## precipation_hanover_train -0.07448607 0.04217725 -1.7660 0.077392 .
## temp_hanover_train -0.00082565 0.00305432 -0.2703 0.786913
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1_hanover <- forecast::forecast(wastewater_weather_mod_1_hanover, h=14,
xreg = vars_test_hanover)
rmse(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.3653023
mae(cases_test_hanover,forecast_mod_1_hanover$mean)
## [1] 0.3033873
checkresiduals(wastewater_weather_mod_1_hanover)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 32.708, df = 3, p-value = 3.71e-07
##
## Model df: 7. Total lags used: 10
wastewater_weather_mod_2_hanover <- Arima(cases_train_hanover ,order = c(4,1,4),
xreg = vars_hanover)
coeftest(wastewater_weather_mod_2_hanover) # weakly insignificant
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.5978171 0.0618578 9.6644 < 2.2e-16 ***
## ar2 -0.5058366 0.0346044 -14.6177 < 2.2e-16 ***
## ar3 1.0158770 0.0356464 28.4987 < 2.2e-16 ***
## ar4 -0.2217023 0.0588369 -3.7681 0.0001645 ***
## ma1 -1.1508573 0.0386121 -29.8056 < 2.2e-16 ***
## ma2 0.6855440 0.0233146 29.4041 < 2.2e-16 ***
## ma3 -1.2495320 0.0301081 -41.5015 < 2.2e-16 ***
## ma4 0.8164728 0.0381123 21.4228 < 2.2e-16 ***
## viral_train_hanover 0.0325131 0.0233953 1.3897 0.1646115
## precipation_hanover_train -0.0586727 0.0413577 -1.4187 0.1559967
## temp_hanover_train 0.0022913 0.0029263 0.7830 0.4336315
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_2_hanover <- forecast::forecast(wastewater_weather_mod_2_hanover, h=14,
xreg = vars_test_hanover)
rmse(cases_test_hanover,forecast_mod_2_hanover$mean)
## [1] 0.3493521
mae(cases_test_hanover,forecast_mod_2_hanover$mean)
## [1] 0.250311
checkresiduals(wastewater_weather_mod_2_hanover)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(4,1,4) errors
## Q* = 24.428, df = 3, p-value = 2.033e-05
##
## Model df: 11. Total lags used: 14
exp(forecast_mod_2_hanover$mean[1])
## [1] 1.377212
exp(forecast_mod_2_hanover$lower[1,])
## 80% 95%
## 0.8576265 0.6674302
exp(forecast_mod_2_hanover$upper[1,])
## 80% 95%
## 2.211583 2.841813
exp(forecast_mod_2_hanover$mean[1])-exp(cases_test_hanover[1])
## [1] 0.269004
exp(forecast_mod_2_hanover$mean[7])
## [1] 2.063698
exp(forecast_mod_2_hanover$lower[7,])
## 80% 95%
## 1.1079036 0.7970697
exp(forecast_mod_2_hanover$upper[7,])
## 80% 95%
## 3.844061 5.343133
exp(forecast_mod_2_hanover$mean[7])-exp(cases_test_hanover[7])
## [1] -0.1947093
exp(forecast_mod_2_hanover$mean[14])
## [1] 2.402687
exp(forecast_mod_2_hanover$lower[14,])
## 80% 95%
## 1.0035497 0.6321565
exp(forecast_mod_2_hanover$upper[14,])
## 80% 95%
## 5.752484 9.132079
exp(forecast_mod_2_hanover$mean[14]) -exp(cases_test_hanover[14])
## [1] 1.56346
hanover_forecast_arimax_weather_plot <- autoplot(forecast_mod_1_hanover) +
autolayer(forecast_mod_1_hanover, series = "Forecasted") +
autolayer(ts(cases_test_hanover,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") +
xlab("Time")+ ggtitle(NULL) + theme(legend.position = "bottom")
SARIMAX- wastewater information only
cases_train_seasonal <- log(cases)[-c(491:504)]
cases_test_seasonal <- log(cases)[c(491:504)]
viral_train_seasonal <- log(viral_gene)[-c(491:504)]
viral_test_seasonal <- log(viral_gene)[c(491:504)]
wastewater_mod_sarimax_wake <- Arima(cases_train_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = viral_train_seasonal)
coeftest(wastewater_mod_sarimax_wake)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.3973303 0.0452715 -8.7766 < 2.2e-16 ***
## ar2 -0.2222987 0.0453107 -4.9061 9.291e-07 ***
## ma1 -1.9646111 0.0107036 -183.5464 < 2.2e-16 ***
## ma2 0.9736454 0.0111200 87.5581 < 2.2e-16 ***
## sar1 -0.9458335 0.0523438 -18.0697 < 2.2e-16 ***
## sma1 -0.0202409 0.0930362 -0.2176 0.8278
## sma2 -0.9671157 0.0904810 -10.6886 < 2.2e-16 ***
## xreg -0.0027061 0.0231074 -0.1171 0.9068
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_wake <- forecast::forecast(wastewater_mod_sarimax_wake, h=14,
xreg = viral_test_seasonal)
rmse(cases_test_seasonal,forecast_sarimax_wake$mean)
## [1] 0.1280255
mae(cases_test_seasonal,forecast_sarimax_wake$mean)
## [1] 0.09187311
checkresiduals(wastewater_mod_sarimax_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 46.219, df = 3, p-value = 5.094e-10
##
## Model df: 8. Total lags used: 11
exp(forecast_sarimax_wake$mean[1])
## [1] 3.182921
exp(forecast_sarimax_wake$lower[1,])
## 80% 95%
## 2.000737 1.564769
exp(forecast_sarimax_wake$upper[1,])
## 80% 95%
## 5.063627 6.474426
exp(forecast_sarimax_wake$mean[1])-exp(cases_test_seasonal[1])
## [1] -1.232079
exp(forecast_sarimax_wake$mean[7])
## [1] 6.020526
exp(forecast_sarimax_wake$lower[7,])
## 80% 95%
## 2.299755 1.381754
exp(forecast_sarimax_wake$upper[7,])
## 80% 95%
## 15.76112 26.23240
exp(forecast_sarimax_wake$mean[7])-exp(cases_test_seasonal[7])
## [1] 0.4755255
exp(forecast_sarimax_wake$mean[14])
## [1] 5.84517
exp(forecast_sarimax_wake$lower[14,])
## 80% 95%
## 1.0264201 0.4086979
exp(forecast_sarimax_wake$upper[14,])
## 80% 95%
## 33.28657 83.59722
exp(forecast_sarimax_wake$mean[14]) -exp(cases_test_seasonal[14])
## [1] 1.323503
#mecklenburg
cases_train_meck_seasonal <- log(cases_meck)[-c(491:504)]
cases_test_meck_seasonal <- log(cases_meck)[c(491:504)]
viral_train_meck_seasonal <- log(viral_gene_meck)[-c(491:504)]
viral_test_meck_seasonal <- log(viral_gene_meck)[c(491:504)]
wastewater_mod_sarimax_meck <- Arima(cases_train_meck_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = viral_train_meck_seasonal,
method = "CSS")
coeftest(wastewater_mod_sarimax_meck)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.446571 0.042218 -10.5777 < 2.2e-16 ***
## ar2 -0.285850 0.038450 -7.4344 1.05e-13 ***
## ma1 -1.960809 0.012689 -154.5225 < 2.2e-16 ***
## ma2 0.967986 0.013115 73.8050 < 2.2e-16 ***
## sar1 -0.852261 0.074714 -11.4070 < 2.2e-16 ***
## sma1 -0.078281 0.079329 -0.9868 0.3237
## sma2 -0.799423 0.075444 -10.5962 < 2.2e-16 ***
## xreg -0.044614 0.030374 -1.4688 0.1419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_meck <- forecast::forecast(wastewater_mod_sarimax_meck, h=14,
xreg = viral_test_meck_seasonal)
rmse(cases_test_meck_seasonal,forecast_sarimax_meck$mean)
## [1] 0.1753461
mae(cases_test_meck_seasonal,forecast_sarimax_meck$mean)
## [1] 0.1423018
checkresiduals(wastewater_mod_sarimax_meck)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 27.449, df = 3, p-value = 4.739e-06
##
## Model df: 8. Total lags used: 11
exp(forecast_sarimax_meck$mean[1])
## [1] 2.594116
exp(forecast_sarimax_meck$lower[1,])
## 80% 95%
## 1.698089 1.356880
exp(forecast_sarimax_meck$upper[1,])
## 80% 95%
## 3.962949 4.959496
exp(forecast_sarimax_meck$mean[1])-exp(cases_test_meck_seasonal[1])
## [1] 0.4874497
exp(forecast_sarimax_meck$mean[7])
## [1] 2.696436
exp(forecast_sarimax_meck$lower[7,])
## 80% 95%
## 1.169503 0.751541
exp(forecast_sarimax_meck$upper[7,])
## 80% 95%
## 6.216972 9.674480
exp(forecast_sarimax_meck$mean[7])-exp(cases_test_meck_seasonal[7])
## [1] -0.09023042
exp(forecast_sarimax_meck$mean[14])
## [1] 2.336227
exp(forecast_sarimax_meck$lower[14,])
## 80% 95%
## 0.5303645 0.2419317
exp(forecast_sarimax_meck$upper[14,])
## 80% 95%
## 10.29095 22.55990
exp(forecast_sarimax_meck$mean[14]) -exp(cases_test_meck_seasonal[14])
## [1] 0.1528934
#new hanover
cases_train_hanover_seasonal <- log(cases_hanover)[-c(491:504)]
cases_test_hanover_seasonal <- log(cases_hanover)[c(491:504)]
viral_train_hanover_seasonal <- log(viral_gene_hanover)[-c(491:504)]
viral_test_hanover_seasonal <- log(viral_gene_hanover)[c(491:504)]
wastewater_mod_sarimax_hanover <- Arima(cases_train_hanover_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = viral_train_hanover_seasonal,method = "CSS")
coeftest(wastewater_mod_sarimax_hanover)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.4220079 0.0438132 -9.6320 < 2.2e-16 ***
## ar2 -0.2284375 0.0441468 -5.1745 2.285e-07 ***
## ma1 -1.9683468 0.0093189 -211.2212 < 2.2e-16 ***
## ma2 0.9738603 0.0096201 101.2314 < 2.2e-16 ***
## sar1 -0.0561730 0.0590202 -0.9518 0.34122
## sma1 -0.7745307 0.0673857 -11.4940 < 2.2e-16 ***
## sma2 -0.1608361 0.0629186 -2.5563 0.01058 *
## xreg 0.0398994 0.0264399 1.5091 0.13128
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_hanover <- forecast::forecast(wastewater_mod_sarimax_hanover, h=14,
xreg = viral_test_hanover_seasonal)
rmse(cases_test_hanover_seasonal,forecast_sarimax_hanover$mean)
## [1] 0.3013065
mae(cases_test_hanover_seasonal,forecast_sarimax_hanover$mean)
## [1] 0.2377347
checkresiduals(wastewater_mod_sarimax_hanover)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 45.095, df = 3, p-value = 8.831e-10
##
## Model df: 8. Total lags used: 11
exp(forecast_sarimax_hanover $mean[1])
## [1] 1.125586
exp(forecast_sarimax_hanover $lower[1,])
## 80% 95%
## 0.6599709 0.4974952
exp(forecast_sarimax_hanover $upper[1,])
## 80% 95%
## 1.919695 2.546643
exp(forecast_sarimax_hanover $mean[1])-exp(cases_test_hanover_seasonal[1])
## [1] 0.3655855
exp(forecast_sarimax_hanover $mean[7])
## [1] 1.335761
exp(forecast_sarimax_hanover $lower[7,])
## 80% 95%
## 0.4628380 0.2640956
exp(forecast_sarimax_hanover $upper[7,])
## 80% 95%
## 3.855035 6.756102
exp(forecast_sarimax_hanover $mean[7])-exp(cases_test_hanover_seasonal[7])
## [1] -0.3192393
exp(forecast_sarimax_hanover $mean[14])
## [1] 1.271932
exp(forecast_sarimax_hanover $lower[14,])
## 80% 95%
## 0.19129868 0.07017355
exp(forecast_sarimax_hanover $upper[14,])
## 80% 95%
## 8.456985 23.054412
exp(forecast_sarimax_hanover $mean[14]) -exp(cases_test_hanover_seasonal[14])
## [1] 0.6569316
SARIMAX modelling- Wastewater and weather information
#wake
vars_weather_wake <- ts.union(viral_train_seasonal,precipation_wake_train,
temp_wake_train)
vars_test_weather_wake <- ts.union(viral_test_seasonal,precipation_wake_test,
temp_wake_test)
wastewater_weather_mod_sarimax_wake <- Arima(cases_train_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = vars_weather_wake)
coeftest(wastewater_weather_mod_sarimax_wake)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.3947980 0.0454890 -8.6790 < 2.2e-16 ***
## ar2 -0.2171876 0.0455792 -4.7651 1.888e-06 ***
## ma1 -1.9668423 0.0105821 -185.8652 < 2.2e-16 ***
## ma2 0.9758908 0.0110089 88.6459 < 2.2e-16 ***
## sar1 -0.3464399 NaN NaN NaN
## sma1 -0.5501228 NaN NaN NaN
## sma2 -0.4497906 NaN NaN NaN
## viral_train_seasonal -0.0026668 0.0234379 -0.1138 0.9094
## precipation_wake_train -0.0143747 0.0445356 -0.3228 0.7469
## temp_wake_train 0.0012620 0.0023898 0.5281 0.5974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_wake <- forecast::forecast(wastewater_weather_mod_sarimax_wake, h=14,
xreg = vars_test_weather_wake)
rmse(cases_test_seasonal,forecast_sarimax_wake$mean)
## [1] 0.150083
mae(cases_test_seasonal,forecast_sarimax_wake$mean)
## [1] 0.1043418
checkresiduals(wastewater_weather_mod_sarimax_wake)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 43.565, df = 3, p-value = 1.867e-09
##
## Model df: 10. Total lags used: 13
exp(forecast_sarimax_wake$mean[1])
## [1] 3.006035
exp(forecast_sarimax_wake$lower[1,])
## 80% 95%
## 1.889125 1.477303
exp(forecast_sarimax_wake$upper[1,])
## 80% 95%
## 4.783295 6.116716
exp(forecast_sarimax_wake$mean[1])-exp(cases_test_seasonal[1])
## [1] -1.408965
exp(forecast_sarimax_wake$mean[7])
## [1] 5.80686
exp(forecast_sarimax_wake$lower[7,])
## 80% 95%
## 2.222236 1.336484
exp(forecast_sarimax_wake$upper[7,])
## 80% 95%
## 15.17374 25.23010
exp(forecast_sarimax_wake$mean[7])-exp(cases_test_seasonal[7])
## [1] 0.26186
exp(forecast_sarimax_wake$mean[14])
## [1] 6.132417
exp(forecast_sarimax_wake$lower[14,])
## 80% 95%
## 1.0251154 0.3976752
exp(forecast_sarimax_wake$upper[14,])
## 80% 95%
## 36.68517 94.56596
exp(forecast_sarimax_wake$mean[14]) -exp(cases_test_seasonal[14])
## [1] 1.61075
#mecklenburg
vars_weather_meck <- ts.union(viral_train_meck_seasonal,precipation_meck_train,
temp_meck_train)
vars_test_weather_meck <- ts.union(viral_test_meck_seasonal,precipation_meck_test,
temp_meck_test)
wastewater_weather_mod_sarimax_meck <- Arima(cases_train_meck_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = vars_weather_meck,method = "CSS")
coeftest(wastewater_weather_mod_sarimax_meck)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.4418382 0.0441232 -10.0137 < 2.2e-16 ***
## ar2 -0.2994553 0.0420548 -7.1206 1.075e-12 ***
## ma1 -1.9568448 0.0142254 -137.5598 < 2.2e-16 ***
## ma2 0.9639982 0.0147059 65.5520 < 2.2e-16 ***
## sar1 -0.7754512 0.1139950 -6.8025 1.028e-11 ***
## sma1 -0.1508841 0.1176689 -1.2823 0.1997
## sma2 -0.7418161 0.1099214 -6.7486 1.493e-11 ***
## viral_train_meck_seasonal -0.0382979 0.0306107 -1.2511 0.2109
## precipation_meck_train -0.0460712 0.0446182 -1.0326 0.3018
## temp_meck_train 0.0032167 0.0024988 1.2873 0.1980
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_meck <- forecast::forecast(wastewater_weather_mod_sarimax_meck, h=14,
xreg = vars_test_weather_meck)
rmse(cases_test_meck_seasonal,forecast_sarimax_meck$mean)
## [1] 0.2329247
mae(cases_test_meck_seasonal,forecast_sarimax_meck$mean)
## [1] 0.21248
checkresiduals(wastewater_weather_mod_sarimax_meck)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 30.258, df = 3, p-value = 1.218e-06
##
## Model df: 10. Total lags used: 13
exp(forecast_sarimax_meck $mean[1])
## [1] 2.595046
exp(forecast_sarimax_meck $lower[1,])
## 80% 95%
## 1.699160 1.357931
exp(forecast_sarimax_meck $upper[1,])
## 80% 95%
## 3.963290 4.959208
exp(forecast_sarimax_meck $mean[1])-exp(cases_test_meck_seasonal[1])
## [1] 0.4883793
exp(forecast_sarimax_meck $mean[7])
## [1] 2.914913
exp(forecast_sarimax_meck $lower[7,])
## 80% 95%
## 1.2573590 0.8056602
exp(forecast_sarimax_meck $upper[7,])
## 80% 95%
## 6.757593 10.546283
exp(forecast_sarimax_meck $mean[7])-exp(cases_test_meck_seasonal[7])
## [1] 0.1282467
exp(forecast_sarimax_meck $mean[14])
## [1] 2.751167
exp(forecast_sarimax_meck$lower[14,])
## 80% 95%
## 0.6101067 0.2748781
exp(forecast_sarimax_meck $upper[14,])
## 80% 95%
## 12.40590 27.53556
exp(forecast_sarimax_meck $mean[14]) -exp(cases_test_meck_seasonal[14])
## [1] 0.5678341
#new hanover
vars_weather_hanover <- ts.union(viral_train_hanover_seasonal,precipation_hanover_train,
temp_hanover_train)
vars_test_weather_hanover <- ts.union(viral_test_hanover_seasonal,precipation_hanover_test,
temp_hanover_test)
wastewater_weather_mod_sarimax_hanover <- Arima(cases_train_hanover_seasonal,
order = c(2,3,2),
seasonal = list(order=c(1,1,2),period=7),
xreg = vars_weather_hanover,method = "CSS") #rain is significant
coeftest(wastewater_weather_mod_sarimax_hanover)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.4299720 0.0415283 -10.3537 < 2.2e-16 ***
## ar2 -0.2308377 0.0444947 -5.1880 2.126e-07 ***
## ma1 -1.9685358 0.0092815 -212.0919 < 2.2e-16 ***
## ma2 0.9741181 0.0095571 101.9256 < 2.2e-16 ***
## sar1 0.0376344 0.1097178 0.3430 0.73159
## sma1 -0.8533583 0.1050950 -8.1199 4.667e-16 ***
## sma2 -0.0872731 0.0982642 -0.8881 0.37446
## viral_train_hanover_seasonal 0.0403801 0.0262716 1.5370 0.12429
## precipation_hanover_train -0.1022082 0.0420563 -2.4303 0.01509 *
## temp_hanover_train -0.0010922 0.0026037 -0.4195 0.67487
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_sarimax_hanover <- forecast::forecast(wastewater_weather_mod_sarimax_hanover , h=14,
xreg = vars_test_weather_hanover)
rmse(cases_test_hanover_seasonal,forecast_sarimax_hanover$mean)
## [1] 0.3003834
mae(cases_test_hanover_seasonal,forecast_sarimax_hanover$mean)
## [1] 0.2392708
checkresiduals(wastewater_weather_mod_sarimax_hanover)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,3,2)(1,1,2)[7] errors
## Q* = 50.376, df = 3, p-value = 6.645e-11
##
## Model df: 10. Total lags used: 13
exp(forecast_sarimax_hanover $mean[1])
## [1] 1.125314
exp(forecast_sarimax_hanover $lower[1,])
## 80% 95%
## 0.6612874 0.4990775
exp(forecast_sarimax_hanover $upper[1,])
## 80% 95%
## 1.914948 2.537343
exp(forecast_sarimax_hanover $mean[1])-exp(cases_test_hanover_seasonal[1])
## [1] 0.3653136
exp(forecast_sarimax_hanover $mean[7])
## [1] 1.255077
exp(forecast_sarimax_hanover $lower[7,])
## 80% 95%
## 0.4391986 0.2519209
exp(forecast_sarimax_hanover $upper[7,])
## 80% 95%
## 3.586574 6.252829
exp(forecast_sarimax_hanover $mean[7])-exp(cases_test_hanover_seasonal[7])
## [1] -0.3999231
exp(forecast_sarimax_hanover $mean[14])
## [1] 1.187353
exp(forecast_sarimax_hanover $lower[14,])
## 80% 95%
## 0.17942359 0.06598225
exp(forecast_sarimax_hanover $upper[14,])
## 80% 95%
## 7.857418 21.366444
exp(forecast_sarimax_hanover $mean[14]) -exp(cases_test_hanover_seasonal[14])
## [1] 0.5723525
Autoregressive Distributed Lag Model
#wake
full_cases_wastewater_weather_data <- full_cases_wastewater_weather_data[-c(505,506,507),]
full_cases_wastewater_weather_data <- full_cases_wastewater_weather_data %>%
mutate(log_mean_new_cases = log(mean_new_cases),
log_viral_gene = log(full_viral_gene_copies_per_person))
full_cases_wastewater_weather_data <- full_cases_wastewater_weather_data %>%
mutate(log_mean_new_cases = seasadj(decompose(ts(log_mean_new_cases, frequency=7))),
log_viral_gene = seasadj(decompose(ts(log_viral_gene, frequency=7))))
full_cases_wastewater_weather_data_train <-
full_cases_wastewater_weather_data[-c(491:504),]
full_cases_wastewater_weather_data_test <-
full_cases_wastewater_weather_data[c(491:504),]
lowest_rmse <- Inf
best_mod <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train, p=p,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_test[,7]),h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse){
lowest_rmse<- forecast_acc
best_mod <-mod
}
}
}
lowest_rmse #0.209
## [1] 0.2086657
summary(best_mod) #ARDL(1,13)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.57652 -0.16130 0.01015 0.19819 1.58432
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.8293899 0.2973165 -6.153 1.65e-09 ***
## log_viral_gene.t 0.0484146 0.0277371 1.745 0.0816 .
## log_viral_gene.1 0.0085678 0.0351151 0.244 0.8073
## log_viral_gene.2 -0.0158866 0.0352055 -0.451 0.6520
## log_viral_gene.3 0.0315251 0.0352034 0.896 0.3710
## log_viral_gene.4 -0.0005125 0.0353556 -0.014 0.9884
## log_viral_gene.5 0.0488269 0.0354301 1.378 0.1688
## log_viral_gene.6 0.0044543 0.0354949 0.125 0.9002
## log_viral_gene.7 -0.0420197 0.0354797 -1.184 0.2369
## log_viral_gene.8 0.0078008 0.0354309 0.220 0.8258
## log_viral_gene.9 0.0243878 0.0353034 0.691 0.4900
## log_viral_gene.10 0.0041653 0.0351960 0.118 0.9058
## log_viral_gene.11 0.0531482 0.0352077 1.510 0.1318
## log_viral_gene.12 -0.0761592 0.0351809 -2.165 0.0309 *
## log_viral_gene.13 0.0366936 0.0273371 1.342 0.1802
## log_mean_new_cases.1 0.7723686 0.0305033 25.321 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3619 on 461 degrees of freedom
## Multiple R-squared: 0.8974, Adjusted R-squared: 0.8941
## F-statistic: 268.9 on 15 and 461 DF, p-value: < 2.2e-16
checkresiduals(best_mod)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## -0.0417420903 -0.1369120561 -0.0811557848 0.0435192023 -0.0016408437
## 19 20 21 22 23
## -0.0466036986 0.1573381802 -0.0806377566 -0.1933854745 0.3101505602
## 24 25 26 27 28
## -0.1080494203 -0.0028412471 -0.2665604050 0.4021827208 -0.2839760165
## 29 30 31 32 33
## -0.2712864079 0.3290206437 -0.1017006024 0.1305949022 0.1668407987
## 34 35 36 37 38
## 0.0448190875 -0.2163680309 -0.2750283404 0.2805826917 -0.1613045822
## 39 40 41 42 43
## 0.0237548319 0.0480230126 -0.0337460028 -0.3416568330 -0.0463296676
## 44 45 46 47 48
## -0.0866027853 0.1089414939 -0.0324475677 -0.1849449296 0.0716646630
## 49 50 51 52 53
## -0.3009231769 0.1761465237 -0.1845748377 -0.0376955632 -0.3678322292
## 54 55 56 57 58
## 0.0501868298 0.0747823443 0.0241326923 0.1356912746 -0.1475208265
## 59 60 61 62 63
## -0.2167145002 0.2368083017 0.1929601982 -0.0615718762 0.1445494422
## 64 65 66 67 68
## 0.0673490526 0.2318447961 -0.0391711425 0.0989738831 0.2611055830
## 69 70 71 72 73
## 0.0607598618 0.2906521259 0.3758893647 -0.0947328765 -0.0233176906
## 74 75 76 77 78
## 0.2258300663 -0.2052906808 0.3033834899 -0.0742531265 0.2128799418
## 79 80 81 82 83
## -0.0012326035 -0.0569668744 -0.3010897423 0.0983904446 -0.1307668221
## 84 85 86 87 88
## 0.1301565258 0.2880814023 -0.4506209383 -0.0339348136 0.2310911786
## 89 90 91 92 93
## -0.2921921745 -0.3837856584 0.0510435751 0.5398327032 0.3230214154
## 94 95 96 97 98
## -0.0111990534 -0.0154002712 0.3140009465 0.1365612275 0.2043764052
## 99 100 101 102 103
## 0.3393487500 -0.4196847501 0.2239302083 -0.1418005133 0.0734271888
## 104 105 106 107 108
## -0.0031750457 0.0347172298 0.0626419069 0.0342815316 -0.1211320123
## 109 110 111 112 113
## 0.0541302968 0.1666334451 -0.0399103753 0.2543234763 0.2456179424
## 114 115 116 117 118
## -0.0231691384 0.0548536211 0.0897910387 -0.0187026153 0.2036108366
## 119 120 121 122 123
## -0.1938760213 0.4699144839 -0.3238426089 0.3118557660 -0.0514199559
## 124 125 126 127 128
## 0.1991516566 -0.0507167072 0.1376719697 0.3230301430 0.0255712962
## 129 130 131 132 133
## 0.2578087262 0.3273859857 0.0177462481 0.3556702852 0.0545730849
## 134 135 136 137 138
## 0.2748981049 0.1191885822 0.5697755582 -0.1110192663 0.3421205998
## 139 140 141 142 143
## -0.1226349489 0.4226971580 0.4120763796 -0.1490102836 0.2916516294
## 144 145 146 147 148
## -0.2427905719 0.0074471904 -0.0321244679 0.1161896650 0.3543573614
## 149 150 151 152 153
## -1.4051591731 0.4609759708 -1.2150272598 0.4569726822 0.3660877872
## 154 155 156 157 158
## 0.0736287475 0.2354941145 -0.7803499279 -0.1869356537 -0.1567051848
## 159 160 161 162 163
## -0.0228174161 -0.4698843322 0.1772091018 -0.2565636090 0.3835435963
## 164 165 166 167 168
## -0.0875063418 0.0141112213 -0.0932070545 0.2068339998 -0.1245688146
## 169 170 171 172 173
## -0.2461291335 -0.2106265673 0.1337901606 -0.7539476665 0.2267374761
## 174 175 176 177 178
## -0.3671512347 0.3398769865 -0.2095862734 -0.2500480979 -0.3606676615
## 179 180 181 182 183
## -0.1927440440 0.0715092358 -0.0129852443 -0.3684919557 -1.8022742628
## 184 185 186 187 188
## 0.9374304282 -0.1042708185 -0.1418902838 -0.1578875076 0.2557876255
## 189 190 191 192 193
## -0.1564654522 0.0502398243 -0.0111697088 0.0995915432 -0.3831805874
## 194 195 196 197 198
## 0.3732083778 -0.2070252711 0.0054438357 0.2273607948 -0.1851797459
## 199 200 201 202 203
## 0.4965422249 -0.1820921641 0.3835561902 -0.0174186630 0.1186078126
## 204 205 206 207 208
## 0.4620427073 -0.0538773460 -0.0073503477 -0.0377942311 0.4212510944
## 209 210 211 212 213
## 0.0351436843 0.0143221089 0.0133230216 0.1506924911 -0.0732146581
## 214 215 216 217 218
## 0.0565770077 0.2923077294 -0.1968382447 0.0720834037 0.1827291257
## 219 220 221 222 223
## 0.0163983116 0.0065368839 -0.0161041785 0.2298531512 -0.0141333796
## 224 225 226 227 228
## -0.0356840784 0.0620217030 0.1725118143 -0.0290619715 0.1738873934
## 229 230 231 232 233
## 0.1744328708 0.0588796280 0.1473922573 -0.0506241753 0.3650467301
## 234 235 236 237 238
## 0.0105123048 0.2391564876 0.2025762708 0.1782099655 0.6066925814
## 239 240 241 242 243
## -0.4699064989 0.1982762473 -0.0637070384 0.3247311781 0.3362062436
## 244 245 246 247 248
## -0.0653722090 -0.0124316783 -0.6368354247 -1.4071837325 1.3918157282
## 249 250 251 252 253
## -0.3688846272 -0.2060525205 -0.0441966021 -0.0088615750 -0.3701163671
## 254 255 256 257 258
## 0.0099508823 -0.3011100906 0.0540678414 -0.0593648808 -0.1376819899
## 259 260 261 262 263
## 0.0174208465 -0.3841236158 0.0165630297 -0.1778271842 -0.1683936105
## 264 265 266 267 268
## -0.2007279909 0.0365810160 -0.3377930814 -0.4799853623 0.4156396119
## 269 270 271 272 273
## -0.3238152079 -0.1231902060 -0.0585318447 -0.1125978653 0.1281962132
## 274 275 276 277 278
## -0.5899374081 -0.0205667960 -0.2712944676 0.0248145355 -0.1296260118
## 279 280 281 282 283
## 0.6444936511 -0.8025320281 0.4452901692 -0.3820986390 0.0747517168
## 284 285 286 287 288
## 0.4926687499 -0.1494903907 -0.4257235357 -0.2404533865 -0.6329416583
## 289 290 291 292 293
## 0.5813457079 -0.1929994430 0.0922662955 -2.5765239843 0.1028463117
## 294 295 296 297 298
## 1.5843169977 -0.7332322413 0.1456505085 0.0880149229 0.0350335481
## 299 300 301 302 303
## -0.1417491502 0.1228814549 -0.0076348383 -0.5264663534 -0.0489343167
## 304 305 306 307 308
## -0.1303017818 0.0003090705 -0.3466866660 0.1320941090 -0.1133320864
## 309 310 311 312 313
## 0.2663365374 -0.4535447855 -0.9682153034 0.7374317924 -0.4911336400
## 314 315 316 317 318
## 0.4894482864 -0.4021660159 0.1336820654 0.0158665000 -0.2699853463
## 319 320 321 322 323
## 0.2513521206 -0.0157973882 0.1833177813 0.4975719801 -0.0086839980
## 324 325 326 327 328
## 0.1040976013 -0.0183429175 0.0414719477 -0.5951589103 0.4807385122
## 329 330 331 332 333
## 0.3470406853 -0.1866525809 0.4680886781 0.0319947060 0.5325468267
## 334 335 336 337 338
## -0.0905505713 0.1891315399 0.1557188900 0.2388000069 -0.1002797472
## 339 340 341 342 343
## 0.1557599655 -0.0921263945 -0.2667844223 0.3283687195 -0.0496379808
## 344 345 346 347 348
## 0.2058769375 -0.1141916360 -0.2235378751 -0.0241232474 0.0680237209
## 349 350 351 352 353
## 0.1376601310 0.3572567524 0.0089015033 -0.0613286925 0.2305173265
## 354 355 356 357 358
## 0.2813167444 0.5406544581 -0.3814566932 -0.3608459192 1.1521768553
## 359 360 361 362 363
## 0.7330512757 0.5187172790 0.2947534836 0.4130223035 -0.1119429921
## 364 365 366 367 368
## 0.3311350218 0.3317737711 0.5040590744 0.6056026593 0.2473646271
## 369 370 371 372 373
## 0.2938392620 0.1981854549 0.2290407568 -0.3467675258 0.7320017788
## 374 375 376 377 378
## 0.0821233353 0.2723873311 0.1887300647 0.1205609116 -0.1459035478
## 379 380 381 382 383
## -1.2583151036 0.6377162315 0.6372681151 0.0013106804 0.0064903769
## 384 385 386 387 388
## -1.0329973511 -0.7159866741 0.8742278542 0.5515743621 -0.2028719947
## 389 390 391 392 393
## -0.2218632780 -0.0650463132 0.0101539147 -0.5810336463 0.1329577554
## 394 395 396 397 398
## 0.3760437809 -0.2660272083 -0.1108463155 -0.0367582966 0.1458798996
## 399 400 401 402 403
## -0.0052593892 0.0578327783 -0.1981317786 -0.1496768479 0.1474334973
## 404 405 406 407 408
## -0.2485770733 -0.1061939044 0.0232850213 -0.0074653224 0.0189484295
## 409 410 411 412 413
## -0.2056837937 -0.1757078516 0.1379894835 -0.2462304676 -0.1889486846
## 414 415 416 417 418
## 0.2558817230 -0.3026764512 -0.2437830183 -0.2815253453 -0.0914274160
## 419 420 421 422 423
## 0.0105115325 -0.6405113615 0.2059791118 -0.4056586806 -0.2603566237
## 424 425 426 427 428
## 0.0606420781 0.0429674664 -0.7664714500 0.0744346446 0.1809520782
## 429 430 431 432 433
## 0.0273559425 0.0502766821 -0.5315485962 0.4725405057 -0.3414037353
## 434 435 436 437 438
## 0.0216919893 -0.2517964430 0.2858718821 -0.5545715262 0.2511257348
## 439 440 441 442 443
## -0.1602194917 -0.2850642895 -0.0718603947 0.2730619769 0.0090388626
## 444 445 446 447 448
## -0.5912043247 0.1507535115 0.2244142512 -0.2906564518 -0.4290569024
## 449 450 451 452 453
## -0.0286620474 -0.3903306490 0.2573945926 -0.4391753938 -0.0449418303
## 454 455 456 457 458
## 0.3557557140 -0.3917795385 0.1484321931 -0.1296784418 -0.3206768038
## 459 460 461 462 463
## 0.3131271331 -0.2010198021 0.0828836570 0.1902485802 -0.2157183408
## 464 465 466 467 468
## -0.2235392099 0.2295261591 0.2135475376 -0.0092074661 -0.1650120848
## 469 470 471 472 473
## 0.3170934123 -0.1158619491 -0.0368124692 0.1904676658 -0.1610594475
## 474 475 476 477 478
## 0.0178717919 0.0976490303 0.0330803268 0.2252708562 -0.3824507278
## 479 480 481 482 483
## 0.0827837494 0.0415253667 -0.1986518520 0.1385059049 -0.0228448686
## 484 485 486 487 488
## -0.2786497766 0.1569772924 -0.0941576332 0.0169421430 0.1704528206
## 489 490
## -0.1485905883 0.2629694349
mod_ardl113 <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train, p=13,q=1)
summary(mod_ardl113)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.57652 -0.16130 0.01015 0.19819 1.58432
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.8293899 0.2973165 -6.153 1.65e-09 ***
## log_viral_gene.t 0.0484146 0.0277371 1.745 0.0816 .
## log_viral_gene.1 0.0085678 0.0351151 0.244 0.8073
## log_viral_gene.2 -0.0158866 0.0352055 -0.451 0.6520
## log_viral_gene.3 0.0315251 0.0352034 0.896 0.3710
## log_viral_gene.4 -0.0005125 0.0353556 -0.014 0.9884
## log_viral_gene.5 0.0488269 0.0354301 1.378 0.1688
## log_viral_gene.6 0.0044543 0.0354949 0.125 0.9002
## log_viral_gene.7 -0.0420197 0.0354797 -1.184 0.2369
## log_viral_gene.8 0.0078008 0.0354309 0.220 0.8258
## log_viral_gene.9 0.0243878 0.0353034 0.691 0.4900
## log_viral_gene.10 0.0041653 0.0351960 0.118 0.9058
## log_viral_gene.11 0.0531482 0.0352077 1.510 0.1318
## log_viral_gene.12 -0.0761592 0.0351809 -2.165 0.0309 *
## log_viral_gene.13 0.0366936 0.0273371 1.342 0.1802
## log_mean_new_cases.1 0.7723686 0.0305033 25.321 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3619 on 461 degrees of freedom
## Multiple R-squared: 0.8974, Adjusted R-squared: 0.8941
## F-statistic: 268.9 on 15 and 461 DF, p-value: < 2.2e-16
f_ardl113 <- forecast(mod_ardl113,
x= t(full_cases_wastewater_weather_data_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl113$forecasts)
## [1] 0.2086657
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl113$forecasts)
## [1] 0.1920911
checkresiduals(mod_ardl113)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## -0.0417420903 -0.1369120561 -0.0811557848 0.0435192023 -0.0016408437
## 19 20 21 22 23
## -0.0466036986 0.1573381802 -0.0806377566 -0.1933854745 0.3101505602
## 24 25 26 27 28
## -0.1080494203 -0.0028412471 -0.2665604050 0.4021827208 -0.2839760165
## 29 30 31 32 33
## -0.2712864079 0.3290206437 -0.1017006024 0.1305949022 0.1668407987
## 34 35 36 37 38
## 0.0448190875 -0.2163680309 -0.2750283404 0.2805826917 -0.1613045822
## 39 40 41 42 43
## 0.0237548319 0.0480230126 -0.0337460028 -0.3416568330 -0.0463296676
## 44 45 46 47 48
## -0.0866027853 0.1089414939 -0.0324475677 -0.1849449296 0.0716646630
## 49 50 51 52 53
## -0.3009231769 0.1761465237 -0.1845748377 -0.0376955632 -0.3678322292
## 54 55 56 57 58
## 0.0501868298 0.0747823443 0.0241326923 0.1356912746 -0.1475208265
## 59 60 61 62 63
## -0.2167145002 0.2368083017 0.1929601982 -0.0615718762 0.1445494422
## 64 65 66 67 68
## 0.0673490526 0.2318447961 -0.0391711425 0.0989738831 0.2611055830
## 69 70 71 72 73
## 0.0607598618 0.2906521259 0.3758893647 -0.0947328765 -0.0233176906
## 74 75 76 77 78
## 0.2258300663 -0.2052906808 0.3033834899 -0.0742531265 0.2128799418
## 79 80 81 82 83
## -0.0012326035 -0.0569668744 -0.3010897423 0.0983904446 -0.1307668221
## 84 85 86 87 88
## 0.1301565258 0.2880814023 -0.4506209383 -0.0339348136 0.2310911786
## 89 90 91 92 93
## -0.2921921745 -0.3837856584 0.0510435751 0.5398327032 0.3230214154
## 94 95 96 97 98
## -0.0111990534 -0.0154002712 0.3140009465 0.1365612275 0.2043764052
## 99 100 101 102 103
## 0.3393487500 -0.4196847501 0.2239302083 -0.1418005133 0.0734271888
## 104 105 106 107 108
## -0.0031750457 0.0347172298 0.0626419069 0.0342815316 -0.1211320123
## 109 110 111 112 113
## 0.0541302968 0.1666334451 -0.0399103753 0.2543234763 0.2456179424
## 114 115 116 117 118
## -0.0231691384 0.0548536211 0.0897910387 -0.0187026153 0.2036108366
## 119 120 121 122 123
## -0.1938760213 0.4699144839 -0.3238426089 0.3118557660 -0.0514199559
## 124 125 126 127 128
## 0.1991516566 -0.0507167072 0.1376719697 0.3230301430 0.0255712962
## 129 130 131 132 133
## 0.2578087262 0.3273859857 0.0177462481 0.3556702852 0.0545730849
## 134 135 136 137 138
## 0.2748981049 0.1191885822 0.5697755582 -0.1110192663 0.3421205998
## 139 140 141 142 143
## -0.1226349489 0.4226971580 0.4120763796 -0.1490102836 0.2916516294
## 144 145 146 147 148
## -0.2427905719 0.0074471904 -0.0321244679 0.1161896650 0.3543573614
## 149 150 151 152 153
## -1.4051591731 0.4609759708 -1.2150272598 0.4569726822 0.3660877872
## 154 155 156 157 158
## 0.0736287475 0.2354941145 -0.7803499279 -0.1869356537 -0.1567051848
## 159 160 161 162 163
## -0.0228174161 -0.4698843322 0.1772091018 -0.2565636090 0.3835435963
## 164 165 166 167 168
## -0.0875063418 0.0141112213 -0.0932070545 0.2068339998 -0.1245688146
## 169 170 171 172 173
## -0.2461291335 -0.2106265673 0.1337901606 -0.7539476665 0.2267374761
## 174 175 176 177 178
## -0.3671512347 0.3398769865 -0.2095862734 -0.2500480979 -0.3606676615
## 179 180 181 182 183
## -0.1927440440 0.0715092358 -0.0129852443 -0.3684919557 -1.8022742628
## 184 185 186 187 188
## 0.9374304282 -0.1042708185 -0.1418902838 -0.1578875076 0.2557876255
## 189 190 191 192 193
## -0.1564654522 0.0502398243 -0.0111697088 0.0995915432 -0.3831805874
## 194 195 196 197 198
## 0.3732083778 -0.2070252711 0.0054438357 0.2273607948 -0.1851797459
## 199 200 201 202 203
## 0.4965422249 -0.1820921641 0.3835561902 -0.0174186630 0.1186078126
## 204 205 206 207 208
## 0.4620427073 -0.0538773460 -0.0073503477 -0.0377942311 0.4212510944
## 209 210 211 212 213
## 0.0351436843 0.0143221089 0.0133230216 0.1506924911 -0.0732146581
## 214 215 216 217 218
## 0.0565770077 0.2923077294 -0.1968382447 0.0720834037 0.1827291257
## 219 220 221 222 223
## 0.0163983116 0.0065368839 -0.0161041785 0.2298531512 -0.0141333796
## 224 225 226 227 228
## -0.0356840784 0.0620217030 0.1725118143 -0.0290619715 0.1738873934
## 229 230 231 232 233
## 0.1744328708 0.0588796280 0.1473922573 -0.0506241753 0.3650467301
## 234 235 236 237 238
## 0.0105123048 0.2391564876 0.2025762708 0.1782099655 0.6066925814
## 239 240 241 242 243
## -0.4699064989 0.1982762473 -0.0637070384 0.3247311781 0.3362062436
## 244 245 246 247 248
## -0.0653722090 -0.0124316783 -0.6368354247 -1.4071837325 1.3918157282
## 249 250 251 252 253
## -0.3688846272 -0.2060525205 -0.0441966021 -0.0088615750 -0.3701163671
## 254 255 256 257 258
## 0.0099508823 -0.3011100906 0.0540678414 -0.0593648808 -0.1376819899
## 259 260 261 262 263
## 0.0174208465 -0.3841236158 0.0165630297 -0.1778271842 -0.1683936105
## 264 265 266 267 268
## -0.2007279909 0.0365810160 -0.3377930814 -0.4799853623 0.4156396119
## 269 270 271 272 273
## -0.3238152079 -0.1231902060 -0.0585318447 -0.1125978653 0.1281962132
## 274 275 276 277 278
## -0.5899374081 -0.0205667960 -0.2712944676 0.0248145355 -0.1296260118
## 279 280 281 282 283
## 0.6444936511 -0.8025320281 0.4452901692 -0.3820986390 0.0747517168
## 284 285 286 287 288
## 0.4926687499 -0.1494903907 -0.4257235357 -0.2404533865 -0.6329416583
## 289 290 291 292 293
## 0.5813457079 -0.1929994430 0.0922662955 -2.5765239843 0.1028463117
## 294 295 296 297 298
## 1.5843169977 -0.7332322413 0.1456505085 0.0880149229 0.0350335481
## 299 300 301 302 303
## -0.1417491502 0.1228814549 -0.0076348383 -0.5264663534 -0.0489343167
## 304 305 306 307 308
## -0.1303017818 0.0003090705 -0.3466866660 0.1320941090 -0.1133320864
## 309 310 311 312 313
## 0.2663365374 -0.4535447855 -0.9682153034 0.7374317924 -0.4911336400
## 314 315 316 317 318
## 0.4894482864 -0.4021660159 0.1336820654 0.0158665000 -0.2699853463
## 319 320 321 322 323
## 0.2513521206 -0.0157973882 0.1833177813 0.4975719801 -0.0086839980
## 324 325 326 327 328
## 0.1040976013 -0.0183429175 0.0414719477 -0.5951589103 0.4807385122
## 329 330 331 332 333
## 0.3470406853 -0.1866525809 0.4680886781 0.0319947060 0.5325468267
## 334 335 336 337 338
## -0.0905505713 0.1891315399 0.1557188900 0.2388000069 -0.1002797472
## 339 340 341 342 343
## 0.1557599655 -0.0921263945 -0.2667844223 0.3283687195 -0.0496379808
## 344 345 346 347 348
## 0.2058769375 -0.1141916360 -0.2235378751 -0.0241232474 0.0680237209
## 349 350 351 352 353
## 0.1376601310 0.3572567524 0.0089015033 -0.0613286925 0.2305173265
## 354 355 356 357 358
## 0.2813167444 0.5406544581 -0.3814566932 -0.3608459192 1.1521768553
## 359 360 361 362 363
## 0.7330512757 0.5187172790 0.2947534836 0.4130223035 -0.1119429921
## 364 365 366 367 368
## 0.3311350218 0.3317737711 0.5040590744 0.6056026593 0.2473646271
## 369 370 371 372 373
## 0.2938392620 0.1981854549 0.2290407568 -0.3467675258 0.7320017788
## 374 375 376 377 378
## 0.0821233353 0.2723873311 0.1887300647 0.1205609116 -0.1459035478
## 379 380 381 382 383
## -1.2583151036 0.6377162315 0.6372681151 0.0013106804 0.0064903769
## 384 385 386 387 388
## -1.0329973511 -0.7159866741 0.8742278542 0.5515743621 -0.2028719947
## 389 390 391 392 393
## -0.2218632780 -0.0650463132 0.0101539147 -0.5810336463 0.1329577554
## 394 395 396 397 398
## 0.3760437809 -0.2660272083 -0.1108463155 -0.0367582966 0.1458798996
## 399 400 401 402 403
## -0.0052593892 0.0578327783 -0.1981317786 -0.1496768479 0.1474334973
## 404 405 406 407 408
## -0.2485770733 -0.1061939044 0.0232850213 -0.0074653224 0.0189484295
## 409 410 411 412 413
## -0.2056837937 -0.1757078516 0.1379894835 -0.2462304676 -0.1889486846
## 414 415 416 417 418
## 0.2558817230 -0.3026764512 -0.2437830183 -0.2815253453 -0.0914274160
## 419 420 421 422 423
## 0.0105115325 -0.6405113615 0.2059791118 -0.4056586806 -0.2603566237
## 424 425 426 427 428
## 0.0606420781 0.0429674664 -0.7664714500 0.0744346446 0.1809520782
## 429 430 431 432 433
## 0.0273559425 0.0502766821 -0.5315485962 0.4725405057 -0.3414037353
## 434 435 436 437 438
## 0.0216919893 -0.2517964430 0.2858718821 -0.5545715262 0.2511257348
## 439 440 441 442 443
## -0.1602194917 -0.2850642895 -0.0718603947 0.2730619769 0.0090388626
## 444 445 446 447 448
## -0.5912043247 0.1507535115 0.2244142512 -0.2906564518 -0.4290569024
## 449 450 451 452 453
## -0.0286620474 -0.3903306490 0.2573945926 -0.4391753938 -0.0449418303
## 454 455 456 457 458
## 0.3557557140 -0.3917795385 0.1484321931 -0.1296784418 -0.3206768038
## 459 460 461 462 463
## 0.3131271331 -0.2010198021 0.0828836570 0.1902485802 -0.2157183408
## 464 465 466 467 468
## -0.2235392099 0.2295261591 0.2135475376 -0.0092074661 -0.1650120848
## 469 470 471 472 473
## 0.3170934123 -0.1158619491 -0.0368124692 0.1904676658 -0.1610594475
## 474 475 476 477 478
## 0.0178717919 0.0976490303 0.0330803268 0.2252708562 -0.3824507278
## 479 480 481 482 483
## 0.0827837494 0.0415253667 -0.1986518520 0.1385059049 -0.0228448686
## 484 485 486 487 488
## -0.2786497766 0.1569772924 -0.0941576332 0.0169421430 0.1704528206
## 489 490
## -0.1485905883 0.2629694349
mod_ardl1411 <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,
p=11,q=14)
summary(mod_ardl1411)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4613 -0.1434 0.0140 0.1672 1.3165
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.935982 0.311323 -3.006 0.002791 **
## log_viral_gene.t 0.020582 0.026380 0.780 0.435674
## log_viral_gene.1 0.014493 0.033027 0.439 0.661012
## log_viral_gene.2 -0.019663 0.033113 -0.594 0.552942
## log_viral_gene.3 0.023124 0.033200 0.696 0.486477
## log_viral_gene.4 0.003947 0.033226 0.119 0.905501
## log_viral_gene.5 0.027756 0.033143 0.837 0.402769
## log_viral_gene.6 0.011458 0.033188 0.345 0.730062
## log_viral_gene.7 -0.029281 0.033204 -0.882 0.378326
## log_viral_gene.8 -0.008775 0.033144 -0.265 0.791331
## log_viral_gene.9 0.017917 0.033017 0.543 0.587637
## log_viral_gene.10 -0.005994 0.032735 -0.183 0.854791
## log_viral_gene.11 0.013394 0.026259 0.510 0.610240
## log_mean_new_cases.1 0.468930 0.047161 9.943 < 2e-16 ***
## log_mean_new_cases.2 0.109227 0.052173 2.094 0.036860 *
## log_mean_new_cases.3 0.080004 0.052447 1.525 0.127855
## log_mean_new_cases.4 0.110467 0.052580 2.101 0.036205 *
## log_mean_new_cases.5 0.177483 0.053019 3.348 0.000884 ***
## log_mean_new_cases.6 0.036936 0.053668 0.688 0.491663
## log_mean_new_cases.7 0.119539 0.053589 2.231 0.026196 *
## log_mean_new_cases.8 -0.083050 0.053541 -1.551 0.121570
## log_mean_new_cases.9 -0.039005 0.053626 -0.727 0.467391
## log_mean_new_cases.10 0.031823 0.053127 0.599 0.549476
## log_mean_new_cases.11 -0.017356 0.052915 -0.328 0.743074
## log_mean_new_cases.12 -0.084198 0.052775 -1.595 0.111326
## log_mean_new_cases.13 0.033950 0.052741 0.644 0.520085
## log_mean_new_cases.14 -0.073242 0.047306 -1.548 0.122268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3357 on 449 degrees of freedom
## Multiple R-squared: 0.9139, Adjusted R-squared: 0.9089
## F-statistic: 183.4 on 26 and 449 DF, p-value: < 2.2e-16
f_ardl1411 <- forecast(mod_ardl1411,
x= t(full_cases_wastewater_weather_data_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl1411$forecasts)
## [1] 0.2168104
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl1411$forecasts)
## [1] 0.1836546
checkresiduals(mod_ardl1411)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## -0.1842245166 -0.0861296050 -0.0262578456 -0.0064723464 -0.0426762850
## 20 21 22 23 24
## 0.1811373604 0.0175349617 -0.1572505301 0.2730325964 -0.0232214417
## 25 26 27 28 29
## 0.0115445452 -0.2293143393 0.2873347852 -0.2672939781 -0.3355455099
## 30 31 32 33 34
## 0.1390014025 -0.0564782417 0.0875242762 0.2352770838 0.1152006941
## 35 36 37 38 39
## -0.1010711348 -0.2766170270 0.1352443894 -0.2188829882 0.0464003751
## 40 41 42 43 44
## 0.0316241672 0.0445627290 -0.2286396830 -0.0865399301 -0.1053300342
## 45 46 47 48 49
## 0.1426812352 0.0857694957 -0.0791202898 0.0996618059 -0.1839208459
## 50 51 52 53 54
## 0.0674317683 -0.1513743867 -0.0636848500 -0.3993395225 -0.0339924676
## 55 56 57 58 59
## 0.0336237046 0.0765350679 0.1969309729 0.0005172382 -0.2582453244
## 60 61 62 63 64
## 0.1758497019 0.1145688825 -0.1028181764 0.0807199478 0.0316316219
## 65 66 67 68 69
## 0.1327846706 -0.0183215964 0.0226460974 0.2157107123 0.1416170896
## 70 71 72 73 74
## 0.2296614908 0.5055091488 0.0521561970 -0.0974273217 0.0682491883
## 75 76 77 78 79
## -0.3464081267 0.0886740656 -0.0443016793 0.0716764279 0.0534669820
## 80 81 82 83 84
## 0.0212748623 -0.3266746536 0.0637852691 -0.1517854208 0.0437520021
## 85 86 87 88 89
## 0.4045665521 -0.2397558774 -0.0389659308 0.1668886675 -0.3382537203
## 90 91 92 93 94
## -0.5413580162 -0.1546854860 0.3520710326 0.4025921526 0.2095165604
## 95 96 97 98 99
## 0.0551532552 0.4117492477 0.2310340573 0.0619664336 0.3702852112
## 100 101 102 103 104
## -0.3659996520 -0.0044539364 -0.2820273933 -0.1702610548 -0.1867061572
## 105 106 107 108 109
## 0.0160634174 -0.0503426977 0.1004954227 -0.0847025062 0.0184641120
## 110 111 112 113 114
## 0.1677675811 -0.0045166105 0.1848077407 0.3155652851 0.0017123017
## 115 116 117 118 119
## 0.0201499198 -0.0072897578 -0.1471967533 0.0649892211 -0.2567447290
## 120 121 122 123 124
## 0.3180680699 -0.2578559732 0.1715460277 -0.0407654594 0.2050619264
## 125 126 127 128 129
## -0.1283455165 0.0464472788 0.1646379647 -0.0074208489 0.1114655544
## 130 131 132 133 134
## 0.1886244484 -0.1235962143 0.2089130225 -0.0777261807 0.0897534749
## 135 136 137 138 139
## -0.0392630622 0.3165360728 -0.1363644954 0.1981465552 -0.2215215698
## 140 141 142 143 144
## 0.2475332028 0.3910507079 -0.0781236710 0.1386567604 -0.1735720773
## 145 146 147 148 149
## -0.1667882723 -0.1602864360 -0.0017313771 0.2791168831 -1.2446589545
## 150 151 152 153 154
## 0.2010499865 -1.2316012038 0.1208550083 0.3942390124 0.3643330889
## 155 156 157 158 159
## 0.5994139528 -0.2251040535 -0.2553868236 -0.2098719206 -0.1423459045
## 160 161 162 163 164
## -0.6261824990 0.0746145589 -0.1036221899 0.3266902752 0.2285167608
## 165 166 167 168 169
## 0.1345033423 0.0234848398 0.3921030542 -0.1310248709 -0.2888057455
## 170 171 172 173 174
## -0.3346308722 -0.0178046585 -0.8237569096 0.0537727478 -0.2987336735
## 175 176 177 178 179
## 0.3920360799 0.0049644440 0.0364454745 -0.2400235480 -0.0319620907
## 180 181 182 183 184
## 0.0896111419 0.2158452519 -0.2042719776 -1.6466917035 0.5637835021
## 185 186 187 188 189
## 0.1385859502 -0.0084976133 0.1187905948 0.5661215724 0.1774999216
## 190 191 192 193 194
## 0.2929252839 -0.0722941997 0.0985391970 -0.3036262277 0.1865300795
## 195 196 197 198 199
## -0.3665561072 -0.0762739724 0.0135137090 -0.1920264988 0.3074981255
## 200 201 202 203 204
## -0.0088667829 0.3391955387 0.1045959119 0.2588369218 0.4291785045
## 205 206 207 208 209
## 0.0204098280 0.0184465190 -0.1104780230 0.2697034265 0.0028814696
## 210 211 212 213 214
## 0.0419644738 -0.0979494161 0.0868746075 -0.0970305611 -0.0670294633
## 215 216 217 218 219
## 0.1908512811 -0.1512890871 0.0255835992 0.1600611619 0.0034475921
## 220 221 222 223 224
## 0.0071120902 -0.0360415240 0.1586572222 0.0035606793 -0.0502878792
## 225 226 227 228 229
## -0.0403038784 0.1481848140 -0.0374356098 0.1107976213 0.1553037386
## 230 231 232 233 234
## 0.0477814486 0.1110411713 -0.1146757342 0.1969397528 -0.0027768938
## 235 236 237 238 239
## 0.1218550071 0.1514320783 0.1669940784 0.5912327499 -0.3766883900
## 240 241 242 243 244
## -0.0495979019 -0.1857916574 0.0988654429 0.2507321225 0.0135622288
## 245 246 247 248 249
## 0.0403873215 -0.5696748039 -1.5865873446 0.8919220254 -0.0822760186
## 250 251 252 253 254
## -0.0485748516 0.1630222222 0.3354818448 -0.2243762717 0.2646385836
## 255 256 257 258 259
## -0.4599378306 0.0119103222 0.1172958366 -0.0926178044 -0.0267898997
## 260 261 262 263 264
## -0.1741233441 -0.1423067638 -0.1683154951 -0.1076029647 -0.1993887590
## 265 266 267 268 269
## 0.0540048422 -0.2140946861 -0.4465152427 0.3935122069 -0.1229999148
## 270 271 272 273 274
## -0.0328911277 0.0831043035 0.0088594194 0.2488088994 -0.4089294928
## 275 276 277 278 279
## -0.1256825061 -0.2582741964 0.0213734176 -0.1355973731 0.7013449295
## 280 281 282 283 284
## -0.5002528665 0.4247785975 -0.2138842822 0.0249356409 0.4448587183
## 285 286 287 288 289
## 0.0732101229 -0.5124918716 -0.2490751165 -0.8424235208 0.2542447174
## 290 291 292 293 294
## -0.1568516733 0.1218880097 -2.4612987995 -0.3886303267 1.3165076657
## 295 296 297 298 299
## -0.1859296201 0.3581716204 0.6624890484 0.4770345997 0.2447427935
## 300 301 302 303 304
## 0.1344935681 -0.1787336647 -0.4601851144 -0.2134567950 -0.4630961972
## 305 306 307 308 309
## -0.1233729125 -0.4058441082 -0.0100965875 -0.0275912750 0.4892245503
## 310 311 312 313 314
## -0.2338331408 -0.9068582252 0.5513015642 -0.2406651326 0.4263839840
## 315 316 317 318 319
## -0.0683218294 0.2782753622 0.2140733302 -0.0657137151 0.1132415097
## 320 321 322 323 324
## -0.0196968837 0.0981828093 0.3842594035 -0.0561284384 0.0528987035
## 325 326 327 328 329
## -0.1754615429 -0.0856128581 -0.8145438611 0.1628236104 0.2825244641
## 330 331 332 333 334
## -0.0932301332 0.4279563417 0.2885995685 0.6202084727 0.1442063807
## 335 336 337 338 339
## 0.2764556537 0.0930344340 0.2241364101 -0.2362858700 0.0067862220
## 340 341 342 343 344
## -0.2526058306 -0.4311946803 0.1250792613 -0.0502285029 0.1786453660
## 345 346 347 348 349
## -0.0041684222 -0.1812127409 -0.0435386339 0.1040552939 0.1810831655
## 350 351 352 353 354
## 0.4964302549 0.2409475717 0.1230553936 0.2875661810 0.3296716572
## 355 356 357 358 359
## 0.5192556035 -0.2530760536 -0.5321046695 0.8648383778 0.8765670332
## 360 361 362 363 364
## 0.6149859799 0.4784652088 0.4985655865 -0.1843786068 0.0531959389
## 365 366 367 368 369
## -0.1285329564 0.1558907211 0.4319776920 0.1746592239 0.1331990611
## 370 371 372 373 374
## 0.1347729451 -0.0423535777 -0.5918717364 0.3549544233 -0.0123358534
## 375 376 377 378 379
## 0.1023419808 0.1924829564 0.1458843414 -0.1942461881 -1.2173498271
## 380 381 382 383 384
## 0.1361224701 0.5878242670 0.2082606231 0.1481623289 -0.8667974035
## 385 386 387 388 389
## -0.8770171340 0.4959182988 0.6233906734 -0.0277453856 0.1200462458
## 390 391 392 393 394
## 0.1846111916 0.0467849905 -0.6885086919 -0.1648419290 0.2642455003
## 395 396 397 398 399
## -0.0459592409 -0.1294998468 -0.0403567194 0.0717888017 0.1271250032
## 400 401 402 403 404
## -0.1045780612 -0.0738128574 -0.1548812858 0.0864681465 -0.3137185135
## 405 406 407 408 409
## -0.1977121611 0.0428431925 0.0588420687 0.0402211061 -0.0615905323
## 410 411 412 413 414
## -0.1365868529 0.1686192989 -0.1307640329 -0.2338499171 0.2827024019
## 415 416 417 418 419
## -0.1090935595 -0.2662020349 -0.2987347252 -0.1665490033 -0.0657298500
## 420 421 422 423 424
## -0.5255945312 0.0444977488 -0.2414322739 -0.2191448620 0.0930775880
## 425 426 427 428 429
## 0.1156247530 -0.7156550294 -0.0562302928 0.0976831542 0.1468853897
## 430 431 432 433 434
## 0.1722577857 -0.3585870807 0.4206892342 -0.0683656352 -0.0388879098
## 435 436 437 438 439
## -0.2062300059 0.1821954907 -0.3861866081 0.2023325465 -0.1072643478
## 440 441 442 443 444
## -0.1476424867 -0.1467677394 0.3493979779 0.0729184219 -0.3734969364
## 445 446 447 448 449
## 0.0175852067 0.3319980888 -0.0947587384 -0.3537263700 -0.1194274364
## 450 451 452 453 454
## -0.3513892994 0.2655532502 -0.3212382950 -0.0571953816 0.5528856841
## 455 456 457 458 459
## -0.1372914259 0.2515315767 0.0793066581 -0.2757035685 0.2815006917
## 460 461 462 463 464
## -0.0271778304 0.0318641099 0.2834100289 -0.0124619903 -0.3083795898
## 465 466 467 468 469
## 0.2075704614 0.2075792184 -0.0082125291 -0.1153333569 0.2389948463
## 470 471 472 473 474
## -0.1255877572 -0.0667826630 0.0521944024 -0.1502844440 -0.0495748138
## 475 476 477 478 479
## 0.0630449612 -0.0068500097 0.2853022030 -0.3005589208 -0.0057430159
## 480 481 482 483 484
## 0.0556608136 -0.1472646441 0.0758988594 0.0881283171 -0.2037462741
## 485 486 487 488 489
## 0.1289792378 0.0144332184 0.0072104087 0.2294987017 -0.0123383501
## 490
## 0.2074579792
mod_ardl92 <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,
p=2,q=9)
summary(mod_ardl92 )
##
## Time series regression with "ts" data:
## Start = 10, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.36421 -0.14943 0.01629 0.16652 1.45010
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.67598 0.23205 -2.913 0.003750 **
## log_viral_gene.t 0.02639 0.02498 1.056 0.291347
## log_viral_gene.1 0.01316 0.03187 0.413 0.679773
## log_viral_gene.2 0.01030 0.02521 0.409 0.683028
## log_mean_new_cases.1 0.48306 0.04625 10.444 < 2e-16 ***
## log_mean_new_cases.2 0.12026 0.05128 2.345 0.019432 *
## log_mean_new_cases.3 0.09138 0.05153 1.773 0.076823 .
## log_mean_new_cases.4 0.10696 0.05167 2.070 0.038980 *
## log_mean_new_cases.5 0.17515 0.05112 3.427 0.000665 ***
## log_mean_new_cases.6 0.02968 0.05163 0.575 0.565665
## log_mean_new_cases.7 0.08478 0.05136 1.651 0.099470 .
## log_mean_new_cases.8 -0.10149 0.05095 -1.992 0.046930 *
## log_mean_new_cases.9 -0.08455 0.04554 -1.857 0.063994 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3343 on 468 degrees of freedom
## Multiple R-squared: 0.9119, Adjusted R-squared: 0.9096
## F-statistic: 403.4 on 12 and 468 DF, p-value: < 2.2e-16
f_ardl92 <- forecast(mod_ardl92 ,
x= t(full_cases_wastewater_weather_data_test[,7]),
h=14,
interval = TRUE)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl92$forecasts[,2])
## [1] 0.2526685
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl92$forecasts[,2])
## [1] 0.2293562
checkresiduals(mod_ardl92)
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -2.396407e-02 -3.976665e-02 2.253188e-02 1.126186e-02 -3.456715e-05
## 15 16 17 18 19
## -1.584383e-01 -1.087522e-01 -5.617950e-02 -2.259314e-02 -4.996504e-02
## 20 21 22 23 24
## 1.568234e-01 1.735783e-02 -2.082497e-01 2.457965e-01 -5.157538e-02
## 25 26 27 28 29
## 2.722065e-03 -2.621960e-01 2.818996e-01 -2.949834e-01 -3.035126e-01
## 30 31 32 33 34
## 1.661684e-01 -4.430982e-02 5.693436e-02 1.717116e-01 1.064284e-01
## 35 36 37 38 39
## -1.529803e-01 -2.945897e-01 1.263618e-01 -2.567127e-01 -1.473113e-02
## 40 41 42 43 44
## 5.214441e-02 2.746484e-02 -2.552454e-01 -8.854845e-02 -1.247769e-01
## 45 46 47 48 49
## 1.160506e-01 7.937280e-02 -6.261422e-02 9.856974e-02 -2.195059e-01
## 50 51 52 53 54
## 1.127137e-01 -1.766453e-01 -5.426369e-02 -4.002780e-01 -3.406671e-02
## 55 56 57 58 59
## 5.963782e-02 1.016042e-01 2.000816e-01 2.983519e-03 -2.650524e-01
## 60 61 62 63 64
## 1.486018e-01 1.601307e-01 -1.384878e-01 7.687082e-02 -4.141107e-02
## 65 66 67 68 69
## 1.098705e-01 -3.128669e-02 6.173563e-02 1.494617e-01 7.418673e-02
## 70 71 72 73 74
## 1.644328e-01 4.680422e-01 2.262063e-02 -1.274640e-01 5.006964e-02
## 75 76 77 78 79
## -3.068078e-01 8.782886e-02 -4.406198e-02 -2.869990e-03 5.181883e-03
## 80 81 82 83 84
## 5.072444e-02 -2.090606e-01 1.372967e-01 -1.820851e-01 -1.857852e-02
## 85 86 87 88 89
## 3.443533e-01 -2.852786e-01 2.303650e-02 2.023233e-01 -2.091241e-01
## 90 91 92 93 94
## -5.177255e-01 -1.381966e-01 3.400566e-01 3.701602e-01 2.276316e-01
## 95 96 97 98 99
## 1.177870e-01 3.214996e-01 1.667340e-01 -1.459042e-03 2.712643e-01
## 100 101 102 103 104
## -3.993105e-01 -1.274003e-02 -2.554181e-01 -1.053282e-01 -1.625378e-01
## 105 106 107 108 109
## 5.634557e-02 -2.966006e-02 1.075129e-01 -6.818631e-02 3.926711e-02
## 110 111 112 113 114
## 1.489118e-01 -5.768349e-02 1.701619e-01 2.698320e-01 4.012499e-03
## 115 116 117 118 119
## 6.400294e-03 -2.979161e-02 -1.944667e-01 5.016915e-02 -2.560521e-01
## 120 121 122 123 124
## 3.215355e-01 -2.638250e-01 1.665216e-01 -2.162241e-02 1.748811e-01
## 125 126 127 128 129
## -1.494302e-01 1.042969e-02 2.123463e-01 -2.841083e-03 1.362311e-01
## 130 131 132 133 134
## 1.325026e-01 -1.897168e-01 1.637814e-01 -3.943942e-02 1.827401e-02
## 135 136 137 138 139
## -5.139633e-02 2.554954e-01 -1.630690e-01 1.330048e-01 -2.957152e-01
## 140 141 142 143 144
## 1.841674e-01 2.507736e-01 -1.557800e-01 9.174971e-02 -2.204612e-01
## 145 146 147 148 149
## -1.119750e-01 -2.616129e-01 -6.771456e-02 1.873420e-01 -1.271189e+00
## 150 151 152 153 154
## 2.556409e-01 -1.170900e+00 1.055138e-01 4.032973e-01 3.828688e-01
## 155 156 157 158 159
## 5.568852e-01 -2.625216e-01 -3.221344e-01 -3.517223e-01 -2.326498e-01
## 160 161 162 163 164
## -6.413548e-01 1.490695e-01 -8.621020e-02 4.664573e-01 1.604656e-01
## 165 166 167 168 169
## 1.383717e-01 -2.395036e-02 3.262965e-01 -1.042147e-01 -3.213268e-01
## 170 171 172 173 174
## -3.663798e-01 -6.002995e-02 -7.778285e-01 9.547445e-02 -2.161891e-01
## 175 176 177 178 179
## 4.416636e-01 6.852906e-02 3.004097e-02 -2.704458e-01 -7.407742e-02
## 180 181 182 183 184
## 4.190433e-02 1.797658e-01 -2.287042e-01 -1.620557e+00 7.144359e-01
## 185 186 187 188 189
## 2.002879e-01 1.150878e-01 1.289638e-01 6.242632e-01 2.050394e-01
## 190 191 192 193 194
## 3.527073e-01 -1.933211e-02 7.994148e-02 -3.369943e-01 1.785146e-01
## 195 196 197 198 199
## -2.045247e-01 2.162620e-03 2.513039e-01 -2.552056e-02 3.232862e-01
## 200 201 202 203 204
## -6.735815e-02 3.296637e-01 8.652104e-02 2.380897e-01 4.655643e-01
## 205 206 207 208 209
## 8.662858e-02 -1.184034e-02 -9.723711e-02 2.729274e-01 8.313439e-03
## 210 211 212 213 214
## 1.015981e-01 -5.016132e-02 2.061002e-01 -5.190664e-02 1.400110e-02
## 215 216 217 218 219
## 2.209761e-01 -1.501411e-01 5.880174e-02 1.781954e-01 5.708528e-02
## 220 221 222 223 224
## 1.981210e-02 1.167935e-02 1.602544e-01 7.165049e-03 -3.680604e-02
## 225 226 227 228 229
## -5.092278e-03 1.754901e-01 -3.829182e-02 1.375325e-01 1.482769e-01
## 230 231 232 233 234
## 5.776840e-02 1.493228e-01 -9.650623e-02 2.228080e-01 -4.609739e-02
## 235 236 237 238 239
## 9.670582e-02 1.313394e-01 1.672115e-01 5.662791e-01 -3.761859e-01
## 240 241 242 243 244
## -6.367110e-02 -2.081374e-01 9.186764e-02 2.436832e-01 3.653342e-03
## 245 246 247 248 249
## -6.807823e-02 -6.105565e-01 -1.620877e+00 9.680602e-01 1.192657e-03
## 250 251 252 253 254
## -9.628339e-02 1.545319e-01 3.129851e-01 -1.631988e-01 2.493072e-01
## 255 256 257 258 259
## -4.769542e-01 -8.771902e-02 -2.167812e-03 -1.056218e-02 1.022641e-01
## 260 261 262 263 264
## -2.346255e-01 1.379507e-02 -2.023609e-01 -1.173748e-01 -2.047266e-01
## 265 266 267 268 269
## 6.049889e-02 -2.346834e-01 -4.229977e-01 3.988999e-01 -9.839163e-02
## 270 271 272 273 274
## -2.135352e-02 7.741357e-02 1.877729e-02 2.034479e-01 -4.268264e-01
## 275 276 277 278 279
## -1.360064e-01 -2.454923e-01 5.370585e-02 -6.652115e-02 7.476438e-01
## 280 281 282 283 284
## -5.191479e-01 4.549196e-01 -2.347329e-01 2.828300e-02 4.456982e-01
## 285 286 287 288 289
## 3.968121e-02 -4.771259e-01 -2.831081e-01 -7.737644e-01 3.006624e-01
## 290 291 292 293 294
## -1.023992e-01 1.395710e-01 -2.364213e+00 -3.909424e-01 1.450096e+00
## 295 296 297 298 299
## -2.085535e-01 2.979523e-01 6.068575e-01 3.951824e-01 2.037335e-01
## 300 301 302 303 304
## 8.261871e-02 -3.236322e-01 -5.990560e-01 -2.930634e-01 -2.168600e-01
## 305 306 307 308 309
## -4.583283e-02 -3.267313e-01 1.914202e-01 -1.029380e-01 4.824966e-01
## 310 311 312 313 314
## -2.567830e-01 -9.254083e-01 5.238682e-01 -2.883445e-01 4.218525e-01
## 315 316 317 318 319
## -1.152390e-01 2.896990e-01 2.318420e-01 -4.225929e-02 1.206934e-01
## 320 321 322 323 324
## -1.258189e-02 8.128629e-02 5.362193e-01 3.580403e-02 5.387543e-02
## 325 326 327 328 329
## -1.426912e-01 -2.952867e-01 -7.912501e-01 1.631587e-01 4.219926e-01
## 330 331 332 333 334
## 6.565432e-02 4.054452e-01 2.009018e-01 4.716507e-01 2.343397e-02
## 335 336 337 338 339
## 2.490811e-01 5.407757e-02 2.453663e-01 -2.296027e-01 3.777055e-02
## 340 341 342 343 344
## -2.720543e-01 -4.027320e-01 2.307273e-01 -3.164816e-02 2.747526e-01
## 345 346 347 348 349
## -4.497552e-03 -1.574489e-01 -4.906954e-02 8.772337e-02 1.370770e-01
## 350 351 352 353 354
## 4.529530e-01 1.906016e-01 1.525708e-01 3.284963e-01 3.650998e-01
## 355 356 357 358 359
## 5.396324e-01 -3.074325e-01 -5.349434e-01 8.777813e-01 9.443478e-01
## 360 361 362 363 364
## 7.003203e-01 4.952868e-01 5.047689e-01 -1.918388e-01 5.261175e-02
## 365 366 367 368 369
## -1.077546e-01 1.598769e-01 4.668144e-01 3.266047e-01 2.771328e-01
## 370 371 372 373 374
## 1.589788e-01 1.313453e-02 -6.308058e-01 3.184335e-01 -6.444854e-03
## 375 376 377 378 379
## 1.939464e-01 1.715339e-01 1.996648e-01 -3.091449e-01 -1.296596e+00
## 380 381 382 383 384
## 1.088063e-01 5.960841e-01 2.713044e-01 2.329620e-01 -8.556874e-01
## 385 386 387 388 389
## -9.022326e-01 4.009147e-01 5.146857e-01 -9.337388e-02 1.724957e-01
## 390 391 392 393 394
## 1.810539e-01 1.784066e-01 -8.606756e-01 -2.221742e-01 1.713428e-01
## 395 396 397 398 399
## -1.589677e-01 -2.242434e-03 6.841561e-02 4.039676e-02 1.309074e-01
## 400 401 402 403 404
## -1.937431e-01 -1.420454e-01 -2.128705e-01 1.629227e-02 -2.543536e-01
## 405 406 407 408 409
## -2.542008e-01 5.524668e-03 3.713062e-02 -3.802828e-02 -8.559204e-02
## 410 411 412 413 414
## -1.088547e-01 9.989792e-02 -1.654432e-01 -3.312310e-01 2.208590e-01
## 415 416 417 418 419
## -1.385087e-01 -2.478310e-01 -2.713380e-01 -1.457082e-01 -6.735750e-02
## 420 421 422 423 424
## -5.499413e-01 1.577297e-02 -2.629274e-01 -2.215989e-01 1.088316e-01
## 425 426 427 428 429
## 1.518798e-01 -7.800507e-01 4.120184e-02 8.104201e-02 1.116859e-01
## 430 431 432 433 434
## 6.589971e-02 -5.915863e-01 3.969890e-01 -1.167412e-01 5.200500e-02
## 435 436 437 438 439
## -1.569589e-01 6.584974e-02 -5.131337e-01 1.382272e-01 -1.724006e-01
## 440 441 442 443 444
## -9.139437e-02 -9.756700e-02 4.205117e-01 9.049092e-02 -4.838474e-01
## 445 446 447 448 449
## 7.527956e-03 3.232683e-01 -1.284454e-01 -3.784562e-01 -9.697398e-02
## 450 451 452 453 454
## -3.759760e-01 3.639162e-01 -2.447045e-01 -3.919063e-02 5.256440e-01
## 455 456 457 458 459
## -1.279611e-01 2.734360e-01 6.062632e-02 -2.399165e-01 3.003080e-01
## 460 461 462 463 464
## -4.265930e-02 5.641235e-02 3.142238e-01 2.458586e-02 -1.890712e-01
## 465 466 467 468 469
## 2.477738e-01 2.543826e-01 8.183976e-02 -1.401468e-01 3.270317e-01
## 470 471 472 473 474
## -8.675708e-02 -2.404920e-02 1.507883e-01 -1.698617e-01 -3.771766e-02
## 475 476 477 478 479
## 9.785553e-02 7.054171e-02 3.302712e-01 -2.662845e-01 8.830143e-03
## 480 481 482 483 484
## 2.716887e-03 -1.649914e-01 1.160813e-01 1.064102e-01 -1.588147e-01
## 485 486 487 488 489
## 1.602108e-01 3.967555e-02 3.183249e-02 2.427844e-01 -4.431468e-03
## 490
## 2.543166e-01
exp(f_ardl92$forecasts[1,2])
## [1] 5.333528
exp(f_ardl92$forecasts[1,1])
## [1] 2.934801
exp(f_ardl92$forecasts[1,3])
## [1] 9.972517
exp(f_ardl92$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_test[1,6])
## [1] -3.384016
exp(f_ardl92$forecasts[7,2])
## [1] 5.891802
exp(f_ardl92$forecasts[7,1])
## [1] 2.248932
exp(f_ardl92$forecasts[7,3])
## [1] 14.95402
exp(f_ardl92$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_test[7,6])
## [1] -1.10645
exp(f_ardl92$forecasts[14,2])
## [1] 6.198724
exp(f_ardl92$forecasts[14,1])
## [1] 2.024789
exp(f_ardl92$forecasts[14,3])
## [1] 19.50234
exp(f_ardl92$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_test[14,6])
## [1] 0.4920041
lowest_rmse_weather <- Inf
best_mod_weather <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
remove <- list(p =list(TAVG=c(1:p),mean_precipation=c(1:p)))
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_train,
p=p,q=q,
remove = remove)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_test[,c(7,4,5)]),h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_weather){
lowest_rmse_weather <- forecast_acc
best_mod_weather <- mod
}
}
}
lowest_rmse_weather #0.20
## [1] 0.2001624
summary(best_mod_weather) #ARDL(13,11)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.43826 -0.14473 0.01622 0.16796 1.37242
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.0012439 0.3182374 -3.146 0.001764 **
## log_viral_gene.t 0.0219351 0.0264055 0.831 0.406583
## log_viral_gene.1 0.0174653 0.0330155 0.529 0.597066
## log_viral_gene.2 -0.0198144 0.0331529 -0.598 0.550363
## log_viral_gene.3 0.0257640 0.0332502 0.775 0.438834
## log_viral_gene.4 -0.0006246 0.0332382 -0.019 0.985016
## log_viral_gene.5 0.0271930 0.0331620 0.820 0.412648
## log_viral_gene.6 0.0135525 0.0331998 0.408 0.683313
## log_viral_gene.7 -0.0291835 0.0332550 -0.878 0.380649
## log_viral_gene.8 -0.0072037 0.0331655 -0.217 0.828149
## log_viral_gene.9 0.0132099 0.0328965 0.402 0.688200
## log_viral_gene.10 -0.0059881 0.0327731 -0.183 0.855105
## log_viral_gene.11 0.0133795 0.0262905 0.509 0.611065
## mean_precipation.t -0.0456209 0.0514223 -0.887 0.375456
## TAVG.t 0.0009141 0.0012119 0.754 0.451100
## log_mean_new_cases.1 0.4663508 0.0472625 9.867 < 2e-16 ***
## log_mean_new_cases.2 0.1182938 0.0522279 2.265 0.023991 *
## log_mean_new_cases.3 0.0779376 0.0526102 1.481 0.139197
## log_mean_new_cases.4 0.1024029 0.0529550 1.934 0.053769 .
## log_mean_new_cases.5 0.1838986 0.0531158 3.462 0.000587 ***
## log_mean_new_cases.6 0.0494224 0.0538579 0.918 0.359298
## log_mean_new_cases.7 0.1092176 0.0534975 2.042 0.041781 *
## log_mean_new_cases.8 -0.0885420 0.0536626 -1.650 0.099647 .
## log_mean_new_cases.9 -0.0536585 0.0530340 -1.012 0.312190
## log_mean_new_cases.10 0.0265351 0.0529905 0.501 0.616791
## log_mean_new_cases.11 -0.0215972 0.0528675 -0.409 0.683090
## log_mean_new_cases.12 -0.0910823 0.0524895 -1.735 0.083383 .
## log_mean_new_cases.13 -0.0010250 0.0475941 -0.022 0.982827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.336 on 449 degrees of freedom
## Multiple R-squared: 0.9139, Adjusted R-squared: 0.9087
## F-statistic: 176.5 on 27 and 449 DF, p-value: < 2.2e-16
remove <- list(p =list(TAVG=c(1:11),mean_precipation=c(1:11)))
mod_ardl1311_weather <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_train,
p=11,q=13,
remove = remove)
summary(mod_ardl1311_weather)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.43826 -0.14473 0.01622 0.16796 1.37242
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.0012439 0.3182374 -3.146 0.001764 **
## log_viral_gene.t 0.0219351 0.0264055 0.831 0.406583
## log_viral_gene.1 0.0174653 0.0330155 0.529 0.597066
## log_viral_gene.2 -0.0198144 0.0331529 -0.598 0.550363
## log_viral_gene.3 0.0257640 0.0332502 0.775 0.438834
## log_viral_gene.4 -0.0006246 0.0332382 -0.019 0.985016
## log_viral_gene.5 0.0271930 0.0331620 0.820 0.412648
## log_viral_gene.6 0.0135525 0.0331998 0.408 0.683313
## log_viral_gene.7 -0.0291835 0.0332550 -0.878 0.380649
## log_viral_gene.8 -0.0072037 0.0331655 -0.217 0.828149
## log_viral_gene.9 0.0132099 0.0328965 0.402 0.688200
## log_viral_gene.10 -0.0059881 0.0327731 -0.183 0.855105
## log_viral_gene.11 0.0133795 0.0262905 0.509 0.611065
## mean_precipation.t -0.0456209 0.0514223 -0.887 0.375456
## TAVG.t 0.0009141 0.0012119 0.754 0.451100
## log_mean_new_cases.1 0.4663508 0.0472625 9.867 < 2e-16 ***
## log_mean_new_cases.2 0.1182938 0.0522279 2.265 0.023991 *
## log_mean_new_cases.3 0.0779376 0.0526102 1.481 0.139197
## log_mean_new_cases.4 0.1024029 0.0529550 1.934 0.053769 .
## log_mean_new_cases.5 0.1838986 0.0531158 3.462 0.000587 ***
## log_mean_new_cases.6 0.0494224 0.0538579 0.918 0.359298
## log_mean_new_cases.7 0.1092176 0.0534975 2.042 0.041781 *
## log_mean_new_cases.8 -0.0885420 0.0536626 -1.650 0.099647 .
## log_mean_new_cases.9 -0.0536585 0.0530340 -1.012 0.312190
## log_mean_new_cases.10 0.0265351 0.0529905 0.501 0.616791
## log_mean_new_cases.11 -0.0215972 0.0528675 -0.409 0.683090
## log_mean_new_cases.12 -0.0910823 0.0524895 -1.735 0.083383 .
## log_mean_new_cases.13 -0.0010250 0.0475941 -0.022 0.982827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.336 on 449 degrees of freedom
## Multiple R-squared: 0.9139, Adjusted R-squared: 0.9087
## F-statistic: 176.5 on 27 and 449 DF, p-value: < 2.2e-16
f_ardl1311_weather <- forecast(mod_ardl1311_weather,
x= t(full_cases_wastewater_weather_data_test[,c(7,4,5)]),
h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl1311_weather$forecasts)
## [1] 0.2001624
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl1311_weather$forecasts)
## [1] 0.1641279
checkresiduals(mod_ardl1311_weather)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18 19
## 0.032061005 -0.150376998 -0.096764266 -0.024326879 -0.006033189 -0.061639427
## 20 21 22 23 24 25
## 0.172313111 0.036109140 -0.163153524 0.306839066 -0.023248073 0.042988574
## 26 27 28 29 30 31
## -0.228792606 0.291939369 -0.253214936 -0.286974412 0.157805177 -0.041882791
## 32 33 34 35 36 37
## 0.092751873 0.248168218 0.120988283 -0.075388784 -0.249685960 0.119038905
## 38 39 40 41 42 43
## -0.226425300 0.024053522 0.092684854 0.049254789 -0.197106402 -0.031675197
## 44 45 46 47 48 49
## -0.085013388 0.154805313 0.122142247 -0.032640348 0.097755610 -0.173631705
## 50 51 52 53 54 55
## 0.102965451 -0.140866728 -0.058196482 -0.403195095 -0.033118074 0.064499978
## 56 57 58 59 60 61
## 0.083693388 0.195087344 0.022111441 -0.245788240 0.172196035 0.130329062
## 62 63 64 65 66 67
## -0.107403410 0.096496264 0.033249704 0.145769693 -0.031483364 0.035262781
## 68 69 70 71 72 73
## 0.210939698 0.122008498 0.222762916 0.486282374 0.054789733 -0.061220550
## 74 75 76 77 78 79
## 0.068447820 -0.342555827 0.109303316 -0.057485398 0.074907367 0.047659920
## 80 81 82 83 84 85
## 0.049316357 -0.303508562 0.049874857 -0.152739977 0.069444011 0.385117934
## 86 87 88 89 90 91
## -0.252648087 -0.040845346 0.186709665 -0.289181694 -0.526622267 -0.154233204
## 92 93 94 95 96 97
## 0.355637101 0.400873761 0.198219842 0.065818752 0.396338656 0.228953050
## 98 99 100 101 102 103
## 0.058659003 0.312909049 -0.382026222 -0.021021910 -0.312984839 -0.177907468
## 104 105 106 107 108 109
## -0.160959236 0.049734977 -0.034218415 0.100279218 -0.080775539 0.041343224
## 110 111 112 113 114 115
## 0.175817973 -0.007346746 0.196050686 0.275538042 0.003330340 -0.009581105
## 116 117 118 119 120 121
## -0.020108093 -0.164347421 0.059155062 -0.265743595 0.301212802 -0.269953292
## 122 123 124 125 126 127
## 0.172284520 -0.027231693 0.208312479 -0.103518220 0.043189146 0.163847678
## 128 129 130 131 132 133
## 0.003105353 0.116445829 0.191607376 -0.103180847 0.202563358 -0.043867650
## 134 135 136 137 138 139
## 0.059618117 -0.036371240 0.305996882 -0.139523286 0.167535828 -0.232367932
## 140 141 142 143 144 145
## 0.231326487 0.357349545 -0.085443014 0.111011907 -0.206700103 -0.175970280
## 146 147 148 149 150 151
## -0.190339179 -0.007742491 0.268882485 -1.239673123 0.177793074 -1.154297496
## 152 153 154 155 156 157
## 0.131496350 0.403115037 0.358667026 0.574829088 -0.240887347 -0.279459683
## 158 159 160 161 162 163
## -0.217093162 -0.128183895 -0.636019502 0.051683543 -0.180209350 0.372307354
## 164 165 166 167 168 169
## 0.179834935 0.196040077 0.050758156 0.369100885 -0.133794298 -0.314467700
## 170 171 172 173 174 175
## -0.350953918 -0.007907322 -0.809125155 0.040713872 -0.261818603 0.401976753
## 176 177 178 179 180 181
## 0.022231672 0.022028720 -0.253000288 -0.057681627 0.112242856 0.213332470
## 182 183 184 185 186 187
## -0.236490610 -1.666117004 0.565193241 0.121877827 0.022131507 0.224330207
## 188 189 190 191 192 193
## 0.617457991 0.183178578 0.274365696 -0.082064447 0.086382726 -0.303353346
## 194 195 196 197 198 199
## 0.172335233 -0.402559087 -0.124805257 0.156135222 -0.159500725 0.309056611
## 200 201 202 203 204 205
## -0.016480849 0.357921288 0.083388823 0.245893505 0.411978780 0.010134125
## 206 207 208 209 210 211
## -0.023043297 -0.111541860 0.239816911 -0.011807657 0.034113355 -0.112054582
## 212 213 214 215 216 217
## 0.106882353 -0.096712172 -0.055318704 0.183312623 -0.140600317 0.043283972
## 218 219 220 221 222 223
## 0.126125438 -0.015719030 -0.015973782 -0.041510343 0.129272034 -0.022913503
## 224 225 226 227 228 229
## -0.045754274 -0.030335738 0.133137226 -0.045719894 0.093117340 0.138695226
## 230 231 232 233 234 235
## 0.051993908 0.098095707 -0.128932499 0.167959783 -0.030371028 0.107488193
## 236 237 238 239 240 241
## 0.115530091 0.136336309 0.565503349 -0.401424554 -0.090609426 -0.205661527
## 242 243 244 245 246 247
## 0.087426181 0.221670423 -0.019028050 0.001623568 -0.592362525 -1.614036292
## 248 249 250 251 252 253
## 0.868355416 -0.087685692 -0.019022951 0.129980643 0.294339087 -0.219017717
## 254 255 256 257 258 259
## 0.221685049 -0.480412584 -0.031807385 0.069297095 -0.136699218 -0.089956797
## 260 261 262 263 264 265
## -0.227832079 -0.032101635 -0.193758911 -0.107770820 -0.219255032 0.036510746
## 266 267 268 269 270 271
## -0.238887761 -0.452834250 0.359906923 -0.128241075 -0.054474895 0.060718711
## 272 273 274 275 276 277
## -0.003573896 0.206321888 -0.431679482 -0.147878048 -0.278433330 0.004269636
## 278 279 280 281 282 283
## -0.145240305 0.795038513 -0.483146613 0.445424917 -0.233729439 0.013174370
## 284 285 286 287 288 289
## 0.426288670 0.046323401 -0.528314549 -0.284140202 -0.815833504 0.247695217
## 290 291 292 293 294 295
## -0.144209513 0.118142450 -2.438256210 -0.433856284 1.372419693 -0.210452936
## 296 297 298 299 300 301
## 0.385413737 0.673003665 0.488546755 0.227292166 0.101759843 -0.230520835
## 302 303 304 305 306 307
## -0.450881823 -0.243036654 -0.478977424 -0.218770399 -0.285253927 0.124793298
## 308 309 310 311 312 313
## -0.060504467 0.520401723 -0.226305752 -0.918235706 0.532619990 -0.248045754
## 314 315 316 317 318 319
## 0.399323330 -0.108377421 0.297233428 0.238884298 -0.061252332 0.093941663
## 320 321 322 323 324 325
## -0.002586508 0.120190993 0.419249838 -0.054135049 0.062405319 -0.088480274
## 326 327 328 329 330 331
## -0.084194447 -0.772760109 0.169526469 0.322643827 -0.075520003 0.422057617
## 332 333 334 335 336 337
## 0.304822179 0.618618225 0.137906359 0.283365138 0.059030578 0.211968946
## 338 339 340 341 342 343
## -0.252468335 0.011854684 -0.241413399 -0.370068490 0.151858385 -0.036801846
## 344 345 346 347 348 349
## 0.212708386 0.006164133 -0.145215431 -0.050753840 0.109360735 0.156216692
## 350 351 352 353 354 355
## 0.488398165 0.258612563 0.144476868 0.303299240 0.335362105 0.551202815
## 356 357 358 359 360 361
## -0.281502103 -0.538542521 0.849285686 0.877310067 0.611771106 0.481068300
## 362 363 364 365 366 367
## 0.515190224 -0.170546097 0.039740992 -0.030973905 0.190796788 0.453644618
## 368 369 370 371 372 373
## 0.200631752 0.121508693 0.171099341 0.054210509 -0.548191005 0.355961935
## 374 375 376 377 378 379
## -0.014790161 0.097820870 0.160768848 0.163398034 -0.166445964 -1.167861458
## 380 381 382 383 384 385
## 0.138438494 0.575983442 0.188435239 0.152091778 -0.845138907 -0.877591360
## 386 387 388 389 390 391
## 0.527000774 0.598915649 -0.049380973 0.110199450 0.199436261 0.019739784
## 392 393 394 395 396 397
## -0.735478112 -0.119181883 0.276424243 -0.072481730 -0.189465299 -0.110170384
## 398 399 400 401 402 403
## 0.093350221 0.207852007 -0.072879502 -0.090193073 -0.176780010 0.065467848
## 404 405 406 407 408 409
## -0.339613881 -0.255417330 0.065369628 0.072541504 0.016215155 -0.072539378
## 410 411 412 413 414 415
## -0.154432700 0.159027761 -0.148005904 -0.260272081 0.266219102 -0.138049227
## 416 417 418 419 420 421
## -0.279057437 -0.322112511 -0.160930245 -0.054283488 -0.527094556 0.047840976
## 422 423 424 425 426 427
## -0.245042592 -0.221495954 0.086591334 0.102312857 -0.714592019 -0.056795039
## 428 429 430 431 432 433
## 0.082415760 0.125096134 0.159796788 -0.349543148 0.417316305 -0.028228935
## 434 435 436 437 438 439
## 0.005114253 -0.234829321 0.163411928 -0.392724810 0.237198533 -0.144727289
## 440 441 442 443 444 445
## -0.127237172 -0.134152750 0.363083941 0.066327482 -0.419665994 0.069049349
## 446 447 448 449 450 451
## 0.327717598 -0.078593109 -0.376452499 -0.112873125 -0.345181157 0.294103245
## 452 453 454 455 456 457
## -0.331954764 -0.027661647 0.567713281 -0.106760640 0.243815109 0.045540692
## 458 459 460 461 462 463
## -0.229800735 0.281965947 -0.033474850 0.020419616 0.296290952 -0.007220395
## 464 465 466 467 468 469
## -0.282857319 0.183976095 0.217966974 0.013014735 -0.141571276 0.259893790
## 470 471 472 473 474 475
## -0.102575592 -0.006328713 0.090598793 -0.155632379 -0.049319827 0.066040565
## 476 477 478 479 480 481
## -0.023419397 0.270277139 -0.293031679 -0.002861828 0.043219488 -0.164362541
## 482 483 484 485 486 487
## 0.086508499 0.057996589 -0.197018256 0.116034046 -0.015890435 -0.002435516
## 488 489 490
## 0.216266189 -0.001900728 0.238943022
remove <- list(p =list(TAVG=c(1:13),mean_precipation=c(1:13)))
mod_ardl813_weather <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_train,
p=13,q=8,
remove = remove)
summary(mod_ardl813_weather)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.39428 -0.14189 0.01805 0.15651 1.37259
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.780751 0.328849 -2.374 0.01800 *
## log_viral_gene.t 0.031172 0.026114 1.194 0.23322
## log_viral_gene.1 0.013489 0.033039 0.408 0.68327
## log_viral_gene.2 -0.022961 0.033116 -0.693 0.48844
## log_viral_gene.3 0.027153 0.033128 0.820 0.41286
## log_viral_gene.4 -0.006753 0.033093 -0.204 0.83841
## log_viral_gene.5 0.035553 0.033149 1.073 0.28406
## log_viral_gene.6 0.019048 0.033086 0.576 0.56509
## log_viral_gene.7 -0.034225 0.033052 -1.035 0.30099
## log_viral_gene.8 -0.012107 0.033056 -0.366 0.71433
## log_viral_gene.9 0.011679 0.032964 0.354 0.72328
## log_viral_gene.10 -0.005044 0.032838 -0.154 0.87799
## log_viral_gene.11 0.051869 0.032833 1.580 0.11485
## log_viral_gene.12 -0.060364 0.032828 -1.839 0.06660 .
## log_viral_gene.13 0.003535 0.026076 0.136 0.89223
## mean_precipation.t -0.042300 0.051342 -0.824 0.41044
## TAVG.t 0.001220 0.001205 1.012 0.31221
## log_mean_new_cases.1 0.486144 0.046723 10.405 < 2e-16 ***
## log_mean_new_cases.2 0.114132 0.051859 2.201 0.02825 *
## log_mean_new_cases.3 0.090453 0.052136 1.735 0.08343 .
## log_mean_new_cases.4 0.093774 0.052026 1.802 0.07214 .
## log_mean_new_cases.5 0.154870 0.052092 2.973 0.00311 **
## log_mean_new_cases.6 0.027813 0.052734 0.527 0.59816
## log_mean_new_cases.7 0.081100 0.052305 1.551 0.12172
## log_mean_new_cases.8 -0.138042 0.047154 -2.927 0.00359 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3363 on 452 degrees of freedom
## Multiple R-squared: 0.9132, Adjusted R-squared: 0.9086
## F-statistic: 198.1 on 24 and 452 DF, p-value: < 2.2e-16
f_ardl813_weather <- forecast(mod_ardl813_weather, x= t(full_cases_wastewater_weather_data_test[,c(7,4,5)]),h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl813_weather$forecasts)
## [1] 0.2383604
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl813_weather$forecasts)
## [1] 0.2170364
checkresiduals(mod_ardl813_weather)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## -0.0051873382 -0.1653064585 -0.1163634279 -0.0375845687 -0.0175413444
## 19 20 21 22 23
## -0.0683182714 0.1664994410 -0.0041764018 -0.1751808550 0.2887896037
## 24 25 26 27 28
## -0.0346758580 0.0278215728 -0.2422329156 0.3188187442 -0.2184220745
## 29 30 31 32 33
## -0.2914196372 0.1528080588 -0.0441128024 0.0797702218 0.2521223999
## 34 35 36 37 38
## 0.1218841956 -0.0996323184 -0.2996064341 0.0964367171 -0.1542556035
## 39 40 41 42 43
## -0.0295945517 0.0943436925 0.0637803014 -0.2604055595 -0.0472540796
## 44 45 46 47 48
## -0.1144520256 0.1575733660 0.0813929507 -0.0276815025 0.1271647948
## 49 50 51 52 53
## -0.1983802153 0.1105048981 -0.1373843596 -0.0735675271 -0.3803912194
## 54 55 56 57 58
## 0.0124732328 0.1094020412 0.1184034964 0.1713610778 0.0104734599
## 59 60 61 62 63
## -0.2214916294 0.1565147162 0.1179143538 -0.0920402990 0.0848260284
## 64 65 66 67 68
## 0.0447030855 0.1974672353 -0.0205232240 0.0104411066 0.1998789744
## 69 70 71 72 73
## 0.0836320513 0.2652872617 0.4583685027 -0.0196192134 -0.1064039827
## 74 75 76 77 78
## 0.0457793081 -0.3509960448 0.1228418338 -0.1280447176 0.1375123067
## 79 80 81 82 83
## 0.0853469572 0.0342799051 -0.3064300906 0.0172416000 -0.2133352522
## 84 85 86 87 88
## 0.1267071847 0.3544217167 -0.2814405836 -0.1178328122 0.2101637301
## 89 90 91 92 93
## -0.2762129034 -0.4700468485 -0.1268623458 0.4059115385 0.4646675521
## 94 95 96 97 98
## 0.1528528079 0.0787409754 0.3706523570 0.1679711186 0.1356300107
## 99 100 101 102 103
## 0.2726857456 -0.4320266015 -0.0133018731 -0.2769595940 -0.1346419615
## 104 105 106 107 108
## -0.1413227260 -0.0307865261 -0.0126902319 0.1163825686 -0.1367884398
## 109 110 111 112 113
## 0.0425386041 0.1371269310 -0.0304701045 0.2029752313 0.2608837757
## 114 115 116 117 118
## -0.0081808528 -0.0218942909 -0.0295312131 -0.1577842448 0.0830081751
## 119 120 121 122 123
## -0.2670651442 0.3227703615 -0.2853897380 0.1882122677 -0.0593486445
## 124 125 126 127 128
## 0.1620758755 -0.1485627376 0.0309397493 0.1334040618 0.0105754533
## 129 130 131 132 133
## 0.0737371692 0.2154714639 -0.0803973775 0.2097987706 -0.0578103353
## 134 135 136 137 138
## 0.0559168700 -0.0453211071 0.3694118359 -0.1954693572 0.1094317289
## 139 140 141 142 143
## -0.3253266427 0.1748081955 0.2715257799 -0.1636542357 0.0730967933
## 144 145 146 147 148
## -0.2895545435 -0.2636586826 -0.2263794305 -0.0690955565 0.2579213860
## 149 150 151 152 153
## -1.2736613389 0.0804444096 -1.1575452461 0.1270645357 0.3821784480
## 154 155 156 157 158
## 0.3631252459 0.4441244745 -0.3328207957 -0.3979061914 -0.1798751643
## 159 160 161 162 163
## -0.2206018779 -0.5771425318 0.1447477529 -0.1751909778 0.5267562612
## 164 165 166 167 168
## 0.1276995551 0.1667923852 -0.0325130820 0.2416780742 -0.1388076396
## 169 170 171 172 173
## -0.2233003975 -0.3601108477 0.0540228086 -0.7453759445 0.0857702308
## 174 175 176 177 178
## -0.2841412809 0.4314751558 0.0547203822 -0.0429921530 -0.3068464038
## 179 180 181 182 183
## -0.1226693674 0.0480735195 0.1957015810 -0.2116218080 -1.6112976360
## 184 185 186 187 188
## 0.6314572207 0.1576141778 0.0910491580 0.2241770584 0.6370442518
## 189 190 191 192 193
## 0.1600776551 0.2977000002 -0.1025107497 0.1906710796 -0.3091179052
## 194 195 196 197 198
## 0.3091661006 -0.1645442821 -0.0147840824 0.2213724219 -0.1177088281
## 199 200 201 202 203
## 0.4038341512 -0.0141317949 0.3579796362 0.0962171505 0.1406160888
## 204 205 206 207 208
## 0.4352171406 0.1041273442 -0.0676165610 -0.0837100932 0.2463939436
## 209 210 211 212 213
## 0.0302954282 -0.0274926655 -0.0502113374 0.1737021082 -0.0837943138
## 214 215 216 217 218
## -0.0077268787 0.2051408619 -0.1237119351 0.0180527670 0.1634375672
## 219 220 221 222 223
## 0.0116094141 -0.0127999991 -0.0527097293 0.1404063676 0.0037636160
## 224 225 226 227 228
## -0.0719122476 -0.0004504518 0.1299758026 -0.0591641618 0.1153344614
## 229 230 231 232 233
## 0.1539395905 0.0641532053 0.0686149730 -0.1229168771 0.1891402473
## 234 235 236 237 238
## -0.0501558667 0.1086664743 0.1297044575 0.1351858713 0.5180724583
## 239 240 241 242 243
## -0.4126949586 -0.0688489444 -0.2372214493 0.0639085113 0.1973365632
## 244 245 246 247 248
## -0.0284356439 -0.0665987015 -0.5988653109 -1.6575008162 0.8801420982
## 249 250 251 252 253
## -0.1664375431 -0.0677627368 0.1332383476 0.2497281305 -0.2711441351
## 254 255 256 257 258
## 0.0090925112 -0.5570103557 0.0636871578 0.0336488116 -0.0272459602
## 259 260 261 262 263
## 0.0700034391 -0.2521988773 -0.0442511905 -0.1001731092 -0.1449781304
## 264 265 266 267 268
## -0.2163418412 0.0479666012 -0.2771770402 -0.4304125595 0.3408008863
## 269 270 271 272 273
## -0.1268765048 -0.0694304445 0.0363978428 -0.0051007387 0.1941851140
## 274 275 276 277 278
## -0.4456793594 -0.1418878726 -0.2272175311 -0.0014621399 -0.0969365037
## 279 280 281 282 283
## 0.8537478644 -0.4983292141 0.4638242742 -0.2822070815 0.0384115307
## 284 285 286 287 288
## 0.4212965207 0.0396252839 -0.4741300867 -0.2119556397 -0.8172032139
## 289 290 291 292 293
## 0.3417350363 -0.1402497508 0.1233461437 -2.3942839623 -0.4291404738
## 294 295 296 297 298
## 1.3725893942 -0.2209286467 0.2973995088 0.6116357370 0.3931781847
## 299 300 301 302 303
## 0.1764194831 0.0037992087 -0.1970102819 -0.4310367426 -0.2506721859
## 304 305 306 307 308
## -0.2010376400 -0.0677549995 -0.3072746859 0.1312025451 0.0223471858
## 309 310 311 312 313
## 0.4418282535 -0.2899685251 -0.9459852229 0.4919761949 -0.2944838206
## 314 315 316 317 318
## 0.4509392582 -0.0845006019 0.2861663766 0.2177041939 -0.0813532082
## 319 320 321 322 323
## 0.0853353293 0.0938177747 0.1085938427 0.5098655904 0.0421073464
## 324 325 326 327 328
## 0.0793070934 -0.0346131007 -0.0461671901 -0.6742921356 0.2408128968
## 329 330 331 332 333
## 0.3372120287 -0.0423324737 0.4621978250 0.2150771126 0.5376169379
## 334 335 336 337 338
## 0.0213225229 0.0632211617 0.0570049633 0.2374807442 -0.1574028638
## 339 340 341 342 343
## 0.1068221213 -0.1940221302 -0.3340268130 0.1238332805 0.0140028059
## 344 345 346 347 348
## 0.2381280215 0.0324723967 -0.1739220327 -0.0736422419 0.0483268164
## 349 350 351 352 353
## 0.0887470767 0.4918377839 0.2713118197 0.1484605854 0.3183614243
## 354 355 356 357 358
## 0.3250672275 0.5693584962 -0.2743996166 -0.4988077412 0.9445885236
## 359 360 361 362 363
## 0.8930693282 0.6844307827 0.5089700001 0.4997961140 -0.1204970646
## 364 365 366 367 368
## 0.0337010488 0.0094604438 0.2829888281 0.5056383526 0.2962405712
## 369 370 371 372 373
## 0.2322465366 0.1538246916 -0.0014974152 -0.5715212328 0.3493452597
## 374 375 376 377 378
## -0.0108281070 0.1539453990 0.1471453783 0.1363654274 -0.1761378458
## 379 380 381 382 383
## -1.2813513284 0.0918190206 0.5983888136 0.1428043264 0.1264316981
## 384 385 386 387 388
## -0.8391078744 -0.9738860292 0.5109593596 0.4516808795 0.0286400081
## 389 390 391 392 393
## 0.0901745677 0.1585294149 0.0841943044 -0.6683807394 -0.2030406792
## 394 395 396 397 398
## 0.2384969009 -0.1390712810 -0.1270707675 -0.0270231052 0.1284710760
## 399 400 401 402 403
## 0.0379955508 -0.0219594934 -0.1695280788 -0.1986080847 0.0334525695
## 404 405 406 407 408
## -0.2926204456 -0.1934232841 -0.0176278140 0.0273915475 0.0325766092
## 409 410 411 412 413
## -0.1181397634 -0.2282183014 0.0973438501 -0.2197736790 -0.2375855473
## 414 415 416 417 418
## 0.2498148389 -0.2043184430 -0.2744414909 -0.3186393395 -0.1675935113
## 419 420 421 422 423
## -0.0096804044 -0.5760188683 0.0793725170 -0.2573768985 -0.2480585593
## 424 425 426 427 428
## 0.0715408880 0.1157720377 -0.7066065351 -0.0867812840 0.0569883563
## 429 430 431 432 433
## 0.0947917481 0.1210998519 -0.3545813336 0.4591536598 -0.0625312590
## 434 435 436 437 438
## -0.0061132219 -0.2725007638 0.2364259393 -0.4822548823 0.2510001141
## 439 440 441 442 443
## -0.1846323061 -0.2436370927 -0.1394006311 0.3610730304 0.1408407562
## 444 445 446 447 448
## -0.4440536058 0.0456577577 0.3197413943 -0.1396650524 -0.3679059246
## 449 450 451 452 453
## -0.0301237031 -0.2638534820 0.2964331899 -0.3556811949 0.0118432188
## 454 455 456 457 458
## 0.5180191008 -0.0852038610 0.2190573660 0.0510070492 -0.2558389243
## 459 460 461 462 463
## 0.3315890975 -0.0066144724 0.1248196722 0.4019280524 -0.0511776886
## 464 465 466 467 468
## -0.1880112413 0.2141152837 0.2201229116 0.0967491989 -0.1180321913
## 469 470 471 472 473
## 0.2831865550 -0.0233968008 0.0160941665 0.1423953231 -0.1018474882
## 474 475 476 477 478
## -0.0092405015 0.1202430617 0.0252630344 0.2573463433 -0.3121834500
## 479 480 481 482 483
## -0.0028087914 0.0633561652 -0.1839499314 0.0900085241 0.0628534532
## 484 485 486 487 488
## -0.2220201055 0.1877685576 -0.0358576711 0.0237494221 0.2100466351
## 489 490
## -0.0624711829 0.3104886852
remove <- list(p =list(TAVG=c(1:14),mean_precipation=c(1:14)))
mod_ardl914_weather <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_train,
p=14,q=9,
remove = remove)
summary(mod_ardl914_weather)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.40290 -0.14197 0.01842 0.15906 1.41266
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.867954 0.335869 -2.584 0.01008 *
## log_viral_gene.t 0.031642 0.026145 1.210 0.22682
## log_viral_gene.1 0.012500 0.033124 0.377 0.70607
## log_viral_gene.2 -0.023609 0.033196 -0.711 0.47733
## log_viral_gene.3 0.025952 0.033267 0.780 0.43573
## log_viral_gene.4 -0.002508 0.033336 -0.075 0.94007
## log_viral_gene.5 0.034824 0.033203 1.049 0.29483
## log_viral_gene.6 0.016574 0.033305 0.498 0.61898
## log_viral_gene.7 -0.033090 0.033232 -0.996 0.31992
## log_viral_gene.8 -0.012193 0.033196 -0.367 0.71357
## log_viral_gene.9 0.009948 0.033083 0.301 0.76378
## log_viral_gene.10 -0.002476 0.033025 -0.075 0.94028
## log_viral_gene.11 0.051209 0.032938 1.555 0.12072
## log_viral_gene.12 -0.060078 0.032996 -1.821 0.06931 .
## log_viral_gene.13 -0.007915 0.033065 -0.239 0.81091
## log_viral_gene.14 0.017932 0.026149 0.686 0.49322
## mean_precipation.t -0.045050 0.051399 -0.876 0.38123
## TAVG.t 0.001150 0.001211 0.949 0.34290
## log_mean_new_cases.1 0.476385 0.047191 10.095 < 2e-16 ***
## log_mean_new_cases.2 0.123148 0.052311 2.354 0.01899 *
## log_mean_new_cases.3 0.089966 0.052254 1.722 0.08581 .
## log_mean_new_cases.4 0.104632 0.052565 1.991 0.04714 *
## log_mean_new_cases.5 0.160262 0.052376 3.060 0.00235 **
## log_mean_new_cases.6 0.032736 0.052929 0.618 0.53657
## log_mean_new_cases.7 0.089809 0.052619 1.707 0.08856 .
## log_mean_new_cases.8 -0.105577 0.052471 -2.012 0.04481 *
## log_mean_new_cases.9 -0.071901 0.047372 -1.518 0.12977
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3364 on 449 degrees of freedom
## Multiple R-squared: 0.9135, Adjusted R-squared: 0.9085
## F-statistic: 182.4 on 26 and 449 DF, p-value: < 2.2e-16
f_ardl914_weather <- forecast(mod_ardl914_weather, x= t(full_cases_wastewater_weather_data_test[,c(7,4,5)]),h=14, interval = TRUE)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl914_weather$forecasts[,2])
## [1] 0.2279778
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_ardl914_weather$forecasts[,2])
## [1] 0.2014719
checkresiduals(mod_ardl914_weather)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## -0.1598551047 -0.1225165616 -0.0301679289 -0.0208382419 -0.0723169834
## 20 21 22 23 24
## 0.1685730951 0.0070409157 -0.1692292859 0.3059135597 -0.0334645403
## 25 26 27 28 29
## 0.0246616435 -0.2479763972 0.3152365404 -0.2246397640 -0.2925211907
## 30 31 32 33 34
## 0.1511805887 -0.0572522361 0.0968126401 0.2632154121 0.1389891099
## 35 36 37 38 39
## -0.1126687887 -0.2812000492 0.1007599223 -0.1795412432 -0.0270208992
## 40 41 42 43 44
## 0.0772433990 0.0694684046 -0.2446254706 -0.0276763095 -0.0892349781
## 45 46 47 48 49
## 0.1347692461 0.1009308698 -0.0313555466 0.1253004386 -0.1931288974
## 50 51 52 53 54
## 0.1142766485 -0.1443105236 -0.0850959969 -0.3892249998 0.0114853287
## 55 56 57 58 59
## 0.1177683209 0.1146963395 0.1803954814 -0.0035036643 -0.2115549331
## 60 61 62 63 64
## 0.1523659667 0.1157369297 -0.1126361059 0.0773482648 0.0419675080
## 65 66 67 68 69
## 0.1963528047 -0.0041495371 0.0252418656 0.1781255163 0.0874398014
## 70 71 72 73 74
## 0.2761932592 0.4527801216 -0.0269581382 -0.1039303667 0.0546314086
## 75 76 77 78 79
## -0.3522411138 0.1072253719 -0.1134907594 0.1375515031 0.1076228497
## 80 81 82 83 84
## 0.0551747713 -0.2914312775 0.0200215046 -0.2016059324 0.1072610916
## 85 86 87 88 89
## 0.3611947058 -0.2967177734 -0.1060418715 0.2254720881 -0.2385084237
## 90 91 92 93 94
## -0.5006965686 -0.1273601464 0.3890071565 0.4452048659 0.1875955743
## 95 96 97 98 99
## 0.0798735963 0.3723132674 0.1906646577 0.1391579161 0.2348353271
## 100 101 102 103 104
## -0.4950425448 -0.0184920863 -0.2620771858 -0.1311337943 -0.1445183473
## 105 106 107 108 109
## -0.0184835067 0.0008695043 0.1410945754 -0.0955488407 0.0404119424
## 110 111 112 113 114
## 0.1528186645 -0.0354792912 0.2036520149 0.2533699211 -0.0102068272
## 115 116 117 118 119
## -0.0179557903 -0.0190902491 -0.1659055829 0.0728095109 -0.2588471366
## 120 121 122 123 124
## 0.3077816170 -0.2780509186 0.2029949600 -0.0425493956 0.1574347118
## 125 126 127 128 129
## -0.1286662381 0.0286641196 0.1526639469 -0.0077900456 0.1067838195
## 130 131 132 133 134
## 0.2133298961 -0.0712961699 0.2065735849 -0.0379197929 0.0470094333
## 135 136 137 138 139
## -0.0453414560 0.3839706948 -0.1897563313 0.0874585831 -0.2874148691
## 140 141 142 143 144
## 0.1806938482 0.3024595124 -0.1373243749 0.0948702093 -0.2780971851
## 145 146 147 148 149
## -0.2323990103 -0.2173007217 -0.0399900874 0.2498237893 -1.2596073938
## 150 151 152 153 154
## 0.1096847620 -1.1282296765 0.1618266313 0.4030587640 0.3794306996
## 155 156 157 158 159
## 0.4521777317 -0.3214800728 -0.3017426112 -0.2315349987 -0.1831764115
## 160 161 162 163 164
## -0.6512397564 0.1016188893 -0.1658488902 0.5320631477 0.1893867020
## 165 166 167 168 169
## 0.1559420518 -0.0238560448 0.2254989572 -0.1329705283 -0.2345259894
## 170 171 172 173 174
## -0.3688520889 -0.0016791787 -0.7335084811 0.0848262881 -0.2762469871
## 175 176 177 178 179
## 0.4251268976 0.1082544641 -0.0260387327 -0.3259783422 -0.1257436967
## 180 181 182 183 184
## 0.0727279454 0.1626047394 -0.2097714256 -1.6266709567 0.6256432427
## 185 186 187 188 189
## 0.1663681233 0.0911628298 0.2253879837 0.6155539970 0.1546327097
## 190 191 192 193 194
## 0.3140108016 -0.0548312269 0.0570171843 -0.3274630483 0.2813735459
## 195 196 197 198 199
## -0.1832264385 -0.0601509779 0.2036643922 -0.1216389817 0.3938849658
## 200 201 202 203 204
## -0.0208546847 0.3566763342 0.0879584789 0.1439236622 0.4242051741
## 205 206 207 208 209
## 0.1216375086 -0.0750703195 -0.1357665603 0.2579409542 0.0095267095
## 210 211 212 213 214
## -0.0258679035 -0.0606696151 0.1908595613 -0.0702991206 -0.0108317933
## 215 216 217 218 219
## 0.2019567514 -0.1472938014 0.0212717739 0.1613945777 0.0276810837
## 220 221 222 223 224
## -0.0231533967 -0.0461885368 0.1333367022 -0.0072548353 -0.0579945543
## 225 226 227 228 229
## -0.0146324119 0.1289198862 -0.0544152067 0.1197575347 0.1582838938
## 230 231 232 233 234
## 0.0574389441 0.0736530017 -0.1263916398 0.1917635144 -0.0563831860
## 235 236 237 238 239
## 0.1054594800 0.1293861842 0.1403057209 0.5255974973 -0.4081098287
## 240 241 242 243 244
## -0.0547901318 -0.2502529804 0.0523296813 0.1992923761 -0.0211109595
## 245 246 247 248 249
## -0.0526225682 -0.5923648641 -1.6034208234 0.8617166269 -0.1366033044
## 250 251 252 253 254
## -0.0753733026 0.1491045660 0.2866682014 -0.2503456919 0.0463365326
## 255 256 257 258 259
## -0.5210128224 -0.0261498079 0.0466911956 -0.0257058195 0.0630534023
## 260 261 262 263 264
## -0.2667616713 -0.0425015436 -0.1205978693 -0.1401521421 -0.2577285786
## 265 266 267 268 269
## 0.0486796698 -0.2734465328 -0.4363797992 0.3658869262 -0.1309025208
## 270 271 272 273 274
## -0.0603408747 0.0357190141 -0.0075485069 0.1841060560 -0.4372974589
## 275 276 277 278 279
## -0.1452598839 -0.2709641177 0.0066672901 -0.1035533810 0.8509232636
## 280 281 282 283 284
## -0.4899937118 0.4447536103 -0.2536189764 0.0103402816 0.4222617360
## 285 286 287 288 289
## 0.0182503708 -0.4878893905 -0.2486933619 -0.7841699623 0.2914797862
## 290 291 292 293 294
## -0.1161855048 0.1079270656 -2.4028952730 -0.4205152574 1.4126643769
## 295 296 297 298 299
## -0.2010308451 0.3252210579 0.5911258621 0.4199844056 0.2029666495
## 300 301 302 303 304
## 0.1026688446 -0.3113853555 -0.5640342023 -0.2255618647 -0.2302023467
## 305 306 307 308 309
## -0.0848028062 -0.3072288604 0.1421825110 0.0295385321 0.4653148025
## 310 311 312 313 314
## -0.2747705195 -0.9408806242 0.4791519963 -0.2958831994 0.4518559305
## 315 316 317 318 319
## -0.0933355497 0.2796988693 0.2059272145 -0.0487177701 0.1105670415
## 320 321 322 323 324
## 0.0185848795 0.1100495594 0.4638978025 0.0464922528 0.0614714762
## 325 326 327 328 329
## -0.0398100947 -0.0454480745 -0.6917372255 0.2288681765 0.3172829818
## 330 331 332 333 334
## -0.0591268650 0.4968998786 0.2243777869 0.5257070882 0.0580607165
## 335 336 337 338 339
## 0.0884957742 0.0187205155 0.2638504302 -0.1418219020 0.0759945435
## 340 341 342 343 344
## -0.2198768254 -0.3543629620 0.1378017026 0.0057710941 0.2672497147
## 345 346 347 348 349
## 0.0418643909 -0.1568855261 -0.0883063410 0.0643899230 0.0949904953
## 350 351 352 353 354
## 0.4701213379 0.2950359043 0.1446385387 0.3203232057 0.3339262169
## 355 356 357 358 359
## 0.5455419438 -0.2966028204 -0.5296154232 0.9101102717 0.9039664027
## 360 361 362 363 364
## 0.6830922666 0.5106395635 0.4811403427 -0.1424008571 0.0514878225
## 365 366 367 368 369
## -0.0136667424 0.1887897764 0.4792338088 0.3156212166 0.2533467269
## 370 371 372 373 374
## 0.1673046628 0.0330032092 -0.5747318501 0.3291672224 -0.0174419297
## 375 376 377 378 379
## 0.1562413692 0.1701293672 0.1575541081 -0.1540578396 -1.2564935345
## 380 381 382 383 384
## 0.0962594584 0.5809421085 0.1709079095 0.1414251990 -0.8290379833
## 385 386 387 388 389
## -0.9572761094 0.5360977090 0.5092223530 -0.0466106074 0.1098035736
## 390 391 392 393 394
## 0.1769070473 0.1132475104 -0.6218903338 -0.2360907553 0.1207579338
## 395 396 397 398 399
## -0.1643837006 -0.0825364288 0.0167049010 0.1356470150 0.0507710700
## 400 401 402 403 404
## -0.0109159064 -0.1758022956 -0.2472423085 0.0739724459 -0.2870882873
## 405 406 407 408 409
## -0.1967654875 -0.0186030947 0.0141095675 0.0593044169 -0.1041403063
## 410 411 412 413 414
## -0.2201607022 0.0965375047 -0.1979194174 -0.2334797314 0.2433807593
## 415 416 417 418 419
## -0.2088143299 -0.2639571698 -0.2999839483 -0.1712260252 -0.0211648734
## 420 421 422 423 424
## -0.5619845374 0.0673473514 -0.2613870199 -0.2327995888 0.0962848637
## 425 426 427 428 429
## 0.1270484552 -0.7137764687 -0.0931071008 0.0626497513 0.0742202975
## 430 431 432 433 434
## 0.1454931697 -0.3461678461 0.4490582422 -0.0496427066 0.0160140915
## 435 436 437 438 439
## -0.2986167052 0.2055632679 -0.4791739946 0.2187411454 -0.1364953791
## 440 441 442 443 444
## -0.2721438772 -0.1104588575 0.4045871484 0.1435415498 -0.4474806112
## 445 446 447 448 449
## 0.0405657595 0.3003622089 -0.1384350711 -0.3655598330 -0.0214074404
## 450 451 452 453 454
## -0.2978741639 0.2919823929 -0.3359265953 -0.0201083441 0.5072172010
## 455 456 457 458 459
## -0.0579247087 0.2381631998 0.0244983684 -0.2372769165 0.2924483937
## 460 461 462 463 464
## -0.0022931343 0.0958687563 0.3655569702 -0.0456459814 -0.2235273489
## 465 466 467 468 469
## 0.2225173991 0.2103193547 0.0623996137 -0.1172026721 0.2644340519
## 470 471 472 473 474
## -0.0437126069 0.0280937499 0.1418535921 -0.1314913335 -0.0261384617
## 475 476 477 478 479
## 0.1250681381 0.0261809836 0.2274880449 -0.2989033067 0.0026326635
## 480 481 482 483 484
## 0.0433829328 -0.1726916006 0.0832219875 0.0580524936 -0.2144775035
## 485 486 487 488 489
## 0.1802469574 -0.0018098246 -0.0056430255 0.2060659052 -0.0612018247
## 490
## 0.2915620203
exp(f_ardl914_weather$forecasts[1,2])
## [1] 5.367364
exp(f_ardl914_weather$forecasts[1,1])
## [1] 2.946514
exp(f_ardl914_weather$forecasts[1,3])
## [1] 9.605158
exp(f_ardl914_weather$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_test[1,6])
## [1] -3.35018
exp(f_ardl914_weather$forecasts[7,2])
## [1] 5.95613
exp(f_ardl914_weather$forecasts[7,1])
## [1] 2.650773
exp(f_ardl914_weather$forecasts[7,3])
## [1] 14.93228
exp(f_ardl914_weather$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_test[7,6])
## [1] -1.042123
exp(f_ardl914_weather$forecasts[14,2])
## [1] 7.352754
exp(f_ardl914_weather$forecasts[14,1])
## [1] 2.502025
exp(f_ardl914_weather$forecasts[14,3])
## [1] 23.27684
exp(f_ardl914_weather$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_test[14,6])
## [1] 1.646034
#Mecklenburg
full_cases_wastewater_weather_data_meck <- full_cases_wastewater_weather_data_meck[-c(505,506,507),]
full_cases_wastewater_weather_data_meck <- full_cases_wastewater_weather_data_meck %>%
mutate(log_mean_new_cases = log(mean_new_cases),
log_viral_gene = log(full_viral_gene_copies_per_person))
full_cases_wastewater_weather_data_meck <- full_cases_wastewater_weather_data_meck %>%
mutate(log_mean_new_cases = seasadj(decompose(ts(log_mean_new_cases, frequency=7))),
log_viral_gene = seasadj(decompose(ts(log_viral_gene, frequency=7))))
full_cases_wastewater_weather_data_meck_train <-
full_cases_wastewater_weather_data_meck[-c(491:504),]
full_cases_wastewater_weather_data_meck_test <-
full_cases_wastewater_weather_data_meck[c(491:504),]
lowest_rmse_meck <- Inf
best_mod_meck <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train, p=p,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_meck_test[,8]),h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_meck){
lowest_rmse_meck<- forecast_acc
best_mod_meck <-mod
}
}
}
lowest_rmse_meck #0.11
## [1] 0.1107693
summary(best_mod_meck) #ARDL(5,1)
##
## Time series regression with "ts" data:
## Start = 6, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7591 -0.1596 0.0036 0.1817 1.1136
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.83391 0.31714 -2.629 0.008829 **
## log_viral_gene.t -0.04353 0.03451 -1.261 0.207770
## log_viral_gene.1 0.09913 0.03463 2.863 0.004383 **
## log_mean_new_cases.1 0.52109 0.04530 11.502 < 2e-16 ***
## log_mean_new_cases.2 0.06677 0.05100 1.309 0.191121
## log_mean_new_cases.3 0.17238 0.05038 3.421 0.000677 ***
## log_mean_new_cases.4 0.06100 0.05080 1.201 0.230452
## log_mean_new_cases.5 0.10279 0.04502 2.283 0.022851 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3132 on 477 degrees of freedom
## Multiple R-squared: 0.9209, Adjusted R-squared: 0.9198
## F-statistic: 793.6 on 7 and 477 DF, p-value: < 2.2e-16
mod_ardl51_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train, p=1,q=5)
summary(mod_ardl51_meck) #wastewater is significant at lagged time t-1
##
## Time series regression with "ts" data:
## Start = 6, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7591 -0.1596 0.0036 0.1817 1.1136
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.83391 0.31714 -2.629 0.008829 **
## log_viral_gene.t -0.04353 0.03451 -1.261 0.207770
## log_viral_gene.1 0.09913 0.03463 2.863 0.004383 **
## log_mean_new_cases.1 0.52109 0.04530 11.502 < 2e-16 ***
## log_mean_new_cases.2 0.06677 0.05100 1.309 0.191121
## log_mean_new_cases.3 0.17238 0.05038 3.421 0.000677 ***
## log_mean_new_cases.4 0.06100 0.05080 1.201 0.230452
## log_mean_new_cases.5 0.10279 0.04502 2.283 0.022851 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3132 on 477 degrees of freedom
## Multiple R-squared: 0.9209, Adjusted R-squared: 0.9198
## F-statistic: 793.6 on 7 and 477 DF, p-value: < 2.2e-16
f_ardl51_meck <- forecast(mod_ardl51_meck , x= t(full_cases_wastewater_weather_data_meck_test[,8]),h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl51_meck$forecasts)
## [1] 0.1107693
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl51_meck$forecasts)
## [1] 0.09374707
checkresiduals(mod_ardl51_meck)
## Time Series:
## Start = 6
## End = 490
## Frequency = 1
## 6 7 8 9 10 11
## -0.144992803 -0.154528950 -0.133926698 0.182971537 -0.054586470 -0.025672398
## 12 13 14 15 16 17
## 0.003600857 0.089782491 -0.004708061 0.025199802 -0.003101377 -0.116164706
## 18 19 20 21 22 23
## -0.168196341 -0.024364651 0.222029565 0.047886939 -0.050931023 -0.138940545
## 24 25 26 27 28 29
## 0.214465000 0.025827523 -0.225926344 -0.070952987 0.202837773 -0.016761819
## 30 31 32 33 34 35
## -0.026726462 0.014734252 -0.224967432 -0.059531178 -0.302987185 0.330717347
## 36 37 38 39 40 41
## 0.033608659 -0.135211554 -0.124342468 -0.240078271 0.055652050 0.118961867
## 42 43 44 45 46 47
## -0.088270625 -0.166181236 0.094532619 -0.106232081 -0.250429346 0.103190486
## 48 49 50 51 52 53
## -0.256810581 0.303153163 -0.235929863 -0.415643589 0.128535816 0.006584904
## 54 55 56 57 58 59
## -0.005906975 -0.078568003 -0.140365117 0.327786636 -0.343437022 0.156674417
## 60 61 62 63 64 65
## -1.036322792 -0.274784371 0.195454625 -0.565710697 0.590719314 0.363041449
## 66 67 68 69 70 71
## 0.099115304 -0.067479514 0.278631327 0.257900498 0.414386778 -0.043795543
## 72 73 74 75 76 77
## -0.007374073 -0.257995332 0.404066428 -0.156858879 0.470228526 0.312996989
## 78 79 80 81 82 83
## 0.295946934 -0.060940902 -0.010522861 -0.119146048 -0.254959730 0.001253895
## 84 85 86 87 88 89
## 0.009725621 0.336664566 -0.246171855 0.359536395 0.003037467 0.201517562
## 90 91 92 93 94 95
## -0.234612105 -0.032931510 0.027308133 -0.350542165 0.027188701 -0.179031042
## 96 97 98 99 100 101
## 0.151804344 0.064175256 -0.022141232 -0.039675842 -0.094652727 0.193928855
## 102 103 104 105 106 107
## -0.079727028 -0.353565133 0.366210572 -0.476732118 0.592983031 -0.066852213
## 108 109 110 111 112 113
## -0.135521183 0.095786686 -0.297134455 0.070047707 0.348012742 -0.131628833
## 114 115 116 117 118 119
## -0.011948338 -0.144414468 -0.440057988 0.331071631 -0.299400679 -0.070169163
## 120 121 122 123 124 125
## -0.130101619 -0.007333190 -0.187350486 -0.020263682 -0.360826411 0.017733707
## 126 127 128 129 130 131
## 0.289677054 -0.272543064 -0.666636399 -0.177430741 -0.898830212 0.110702455
## 132 133 134 135 136 137
## -0.143884596 0.778765330 -0.011133061 0.047667249 -0.372625096 -0.263415463
## 138 139 140 141 142 143
## 0.126560172 -0.427779448 -0.162454304 0.418718268 -0.300359969 -0.579639640
## 144 145 146 147 148 149
## 0.438529036 0.430950455 0.078395787 0.089242473 -0.207584876 -0.321396510
## 150 151 152 153 154 155
## 0.935631706 0.024385520 -0.654667871 -0.320742908 0.624255405 -0.438734676
## 156 157 158 159 160 161
## -0.188115833 -0.190563186 0.389737781 0.147281439 -0.370012084 0.344793461
## 162 163 164 165 166 167
## 0.386640243 0.278368538 0.236444776 -0.289484029 -0.239347323 -0.147775084
## 168 169 170 171 172 173
## 0.421903669 -0.472504641 -0.592796447 -0.398360812 0.205100174 0.015503158
## 174 175 176 177 178 179
## -0.748619246 0.366642728 0.207370920 -0.329533286 0.039462191 -0.348921816
## 180 181 182 183 184 185
## 0.902647851 0.239740997 0.136067113 -0.403975534 0.076238215 -0.257722454
## 186 187 188 189 190 191
## 0.196253637 0.510291413 0.513786053 0.521666601 0.225189039 -0.206571379
## 192 193 194 195 196 197
## 0.218983696 -0.120526134 0.056688808 0.151611857 0.016239988 0.705324127
## 198 199 200 201 202 203
## -0.030912129 0.173137513 0.199105669 0.160386211 0.304621289 0.242804904
## 204 205 206 207 208 209
## 0.216044301 0.091175723 -0.099425313 0.232585680 0.110244477 0.016836381
## 210 211 212 213 214 215
## 0.206028007 0.202335411 0.057424217 -0.172499638 -0.046289502 0.177043374
## 216 217 218 219 220 221
## -0.022717898 -0.137142897 0.182413491 -0.035504820 0.040322229 0.192119224
## 222 223 224 225 226 227
## 0.051986352 0.099150905 -0.256522770 -0.017478788 0.005780314 0.126185096
## 228 229 230 231 232 233
## 0.085020801 0.125825516 0.157224875 0.037575411 0.181811293 0.160002425
## 234 235 236 237 238 239
## -0.144176437 -0.132360134 0.005312516 0.155005045 -0.050772582 -0.061820079
## 240 241 242 243 244 245
## 0.130881559 -0.118542212 -0.265687059 0.100253328 -0.026092595 -0.105632762
## 246 247 248 249 250 251
## 0.006946720 -0.855422488 0.489696495 0.182152765 0.183784260 0.072996289
## 252 253 254 255 256 257
## 0.092604453 -0.207437140 0.113043773 -0.118922586 -0.309382751 -0.005559694
## 258 259 260 261 262 263
## 0.062175309 -0.151915285 -0.209386914 0.041819824 -0.146114434 -0.231540655
## 264 265 266 267 268 269
## 0.064320055 -0.131629585 -0.048747819 -0.288049131 0.103739890 -0.252829716
## 270 271 272 273 274 275
## 0.391770669 -0.065970454 0.131360564 -0.179354336 -0.306677122 0.045238891
## 276 277 278 279 280 281
## -0.059912722 -0.397106445 -0.094034469 0.079267901 -0.303629835 0.024189968
## 282 283 284 285 286 287
## -0.022693476 -0.143050897 0.073425525 -0.136597452 0.168396949 0.053725800
## 288 289 290 291 292 293
## -0.147249882 -0.147967309 -0.364078434 -0.125688530 -1.196700945 -0.282673542
## 294 295 296 297 298 299
## 0.670515901 0.533289970 -0.028610032 0.101910953 0.234739102 -0.406847444
## 300 301 302 303 304 305
## 0.189635572 0.264275301 -0.166644696 -0.002768102 0.008631935 -0.570484138
## 306 307 308 309 310 311
## 0.249815590 -0.073528528 0.200842317 0.043590647 0.075978870 -0.262761353
## 312 313 314 315 316 317
## 0.025882028 -0.030714663 0.122142094 0.096363475 0.284255533 -0.135206941
## 318 319 320 321 322 323
## 0.197810465 0.021309613 0.049463195 -0.073689175 0.151796019 -0.046817494
## 324 325 326 327 328 329
## -0.138715949 0.205704005 -0.024223650 -0.513306660 0.298996982 0.805954156
## 330 331 332 333 334 335
## 0.021648674 0.308777596 -0.065833168 0.212915000 0.041421806 0.473468117
## 336 337 338 339 340 341
## -0.110225950 -0.172449698 0.099445579 -0.134915004 -0.024795992 -0.047601090
## 342 343 344 345 346 347
## 0.124022800 0.068010871 -0.004663416 0.320403573 0.027263164 0.275705782
## 348 349 350 351 352 353
## 0.245434695 0.361830532 0.180135636 0.267686172 0.264712533 0.381481079
## 354 355 356 357 358 359
## 0.429917116 0.399063104 0.013212848 -0.665136847 0.811976751 0.653863118
## 360 361 362 363 364 365
## 0.627484178 0.478597552 0.479212778 -0.112929716 -0.244679814 0.353230629
## 366 367 368 369 370 371
## 0.390134188 0.312537387 0.299665291 0.174226975 -0.072554462 -0.294971350
## 372 373 374 375 376 377
## -0.144349298 0.276618918 0.013716003 0.104845559 0.048590437 0.073137496
## 378 379 380 381 382 383
## -0.288019052 -1.759116418 0.238733695 0.548555331 0.425413105 0.298553523
## 384 385 386 387 388 389
## -0.140345543 -0.542320158 -0.031626245 0.088830281 -0.090736332 -0.068731086
## 390 391 392 393 394 395
## -0.111162495 -0.196964594 -0.319511537 -0.054113044 0.149243114 -0.278231170
## 396 397 398 399 400 401
## 0.107463973 -0.235278606 0.042654836 -0.314788705 -0.159564779 0.165631549
## 402 403 404 405 406 407
## -0.124195848 0.021199812 -0.074856428 0.003123220 -0.194514790 -0.599461655
## 408 409 410 411 412 413
## 0.181716654 -0.365029118 -0.201435520 -0.169902263 -0.025851496 -0.076552159
## 414 415 416 417 418 419
## 0.088030763 -0.099582205 -0.043695050 -0.269273042 -0.275890575 0.453215587
## 420 421 422 423 424 425
## -0.648014612 -1.039674707 0.313312115 -0.458413319 -0.243757085 0.043610984
## 426 427 428 429 430 431
## -0.409536010 -0.647201886 0.725509043 -0.526357990 -0.257236978 -0.320068168
## 432 433 434 435 436 437
## -0.747243395 0.126461863 0.151211756 -0.195650731 -0.435941417 -0.033441117
## 438 439 440 441 442 443
## 0.887763414 -0.354115210 0.066950153 -0.297217749 0.114176726 0.248600861
## 444 445 446 447 448 449
## -0.237119057 0.171923712 0.152815884 -0.274514800 -0.442306864 0.528678067
## 450 451 452 453 454 455
## -0.700643002 1.113551041 0.124461468 -0.002252850 -0.439067637 0.045817052
## 456 457 458 459 460 461
## -0.055935982 0.208110401 -0.026114953 0.292336475 0.195834414 -0.154004131
## 462 463 464 465 466 467
## -0.561091450 0.475967668 0.501946529 0.212726944 0.339048541 0.361194746
## 468 469 470 471 472 473
## -0.414063098 -0.038215609 -0.612293382 0.434307608 0.109741430 0.048668491
## 474 475 476 477 478 479
## 0.153398245 -0.196706260 -0.356587010 0.067284042 0.504891508 -0.059144656
## 480 481 482 483 484 485
## 0.228707726 -0.041757265 -0.061190527 0.050164468 0.042556326 0.204656551
## 486 487 488 489 490
## -0.025643610 0.162770989 0.068308710 0.002701517 0.155538875
mod_ardl84_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,
p=4,q=8)
summary(mod_ardl84_meck)
##
## Time series regression with "ts" data:
## Start = 9, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.78380 -0.15859 -0.00029 0.17472 1.13456
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.64873 0.36787 -1.763 0.078471 .
## log_viral_gene.t -0.05323 0.03506 -1.518 0.129652
## log_viral_gene.1 0.10831 0.04532 2.390 0.017239 *
## log_viral_gene.2 -0.03948 0.04551 -0.868 0.386111
## log_viral_gene.3 0.11034 0.04559 2.420 0.015884 *
## log_viral_gene.4 -0.08245 0.03506 -2.351 0.019112 *
## log_mean_new_cases.1 0.52497 0.04610 11.387 < 2e-16 ***
## log_mean_new_cases.2 0.06068 0.05195 1.168 0.243404
## log_mean_new_cases.3 0.19410 0.05192 3.738 0.000208 ***
## log_mean_new_cases.4 0.06080 0.05200 1.169 0.242904
## log_mean_new_cases.5 0.09745 0.05179 1.882 0.060515 .
## log_mean_new_cases.6 0.06023 0.05126 1.175 0.240619
## log_mean_new_cases.7 -0.01669 0.05107 -0.327 0.743978
## log_mean_new_cases.8 -0.04549 0.04586 -0.992 0.321746
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3129 on 468 degrees of freedom
## Multiple R-squared: 0.9221, Adjusted R-squared: 0.9199
## F-statistic: 426.1 on 13 and 468 DF, p-value: < 2.2e-16
f_ardl84_meck <- forecast(mod_ardl84_meck ,
x= t(full_cases_wastewater_weather_data_meck_test[,8]),
h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl84_meck$forecasts)
## [1] 0.1121279
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl84_meck$forecasts)
## [1] 0.0923158
checkresiduals(mod_ardl84_meck)
## Time Series:
## Start = 9
## End = 490
## Frequency = 1
## 9 10 11 12 13
## 2.114865e-01 -6.412026e-02 5.053977e-02 -4.626028e-02 9.601234e-02
## 14 15 16 17 18
## 4.090677e-03 1.506730e-02 1.295953e-03 -1.121956e-01 -1.720069e-01
## 19 20 21 22 23
## -5.737256e-02 2.566891e-01 5.100448e-02 -4.963672e-02 -1.324656e-01
## 24 25 26 27 28
## 2.314733e-01 -2.187509e-05 -2.651579e-01 -4.760945e-02 2.094540e-01
## 29 30 31 32 33
## -1.507552e-02 -3.481667e-02 -2.679562e-02 -1.458731e-01 -2.444237e-02
## 34 35 36 37 38
## -4.094079e-01 3.307782e-01 4.719045e-02 -1.102542e-01 -1.005338e-01
## 39 40 41 42 43
## -2.676435e-01 5.671593e-02 1.286972e-01 -9.334871e-02 -1.475369e-01
## 44 45 46 47 48
## 1.066811e-01 -9.330449e-02 -2.613879e-01 1.211922e-01 -2.684318e-01
## 49 50 51 52 53
## 3.285657e-01 -2.391886e-01 -4.018863e-01 1.693160e-01 -5.568607e-02
## 54 55 56 57 58
## -2.313547e-02 -1.694647e-02 -1.356441e-01 3.580371e-01 -3.509830e-01
## 59 60 61 62 63
## 1.273845e-01 -9.987574e-01 -2.594677e-01 1.720282e-01 -5.704496e-01
## 64 65 66 67 68
## 5.939196e-01 3.676968e-01 6.256490e-02 1.217482e-01 2.168790e-01
## 69 70 71 72 73
## 2.556702e-01 3.590379e-01 -9.562880e-02 -1.700112e-02 -1.586703e-01
## 74 75 76 77 78
## 1.583908e-01 -1.798964e-01 4.527362e-01 3.285885e-01 3.098914e-01
## 79 80 81 82 83
## -5.546003e-02 -3.923615e-02 -1.424467e-01 -2.703238e-01 -4.731195e-02
## 84 85 86 87 88
## 3.022135e-03 3.533337e-01 -2.273971e-01 3.777404e-01 -1.873153e-02
## 89 90 91 92 93
## 1.863850e-01 -2.208664e-01 -5.344728e-02 2.058851e-02 -3.535054e-01
## 94 95 96 97 98
## -1.115081e-02 -1.180501e-01 1.903608e-01 -4.033137e-03 -2.619214e-02
## 99 100 101 102 103
## -2.682733e-02 -7.661468e-02 1.738754e-01 -4.873295e-02 -3.699302e-01
## 104 105 106 107 108
## 3.505812e-01 -4.764005e-01 6.032767e-01 -8.084726e-02 -1.440491e-01
## 109 110 111 112 113
## 1.318371e-01 -3.443232e-01 9.853675e-02 3.201137e-01 -1.583409e-01
## 114 115 116 117 118
## 1.797709e-02 -1.638852e-01 -4.143736e-01 3.578324e-01 -4.115361e-01
## 119 120 121 122 123
## -4.911202e-02 -1.236707e-01 1.852453e-02 -1.762155e-01 1.838990e-02
## 124 125 126 127 128
## -3.910660e-01 2.462672e-02 2.955379e-01 -2.829274e-01 -6.436189e-01
## 129 130 131 132 133
## -2.607332e-01 -7.460666e-01 7.716380e-02 -1.372747e-01 7.826791e-01
## 134 135 136 137 138
## 3.990627e-02 6.306165e-02 -3.154304e-01 -3.635332e-01 1.025547e-01
## 139 140 141 142 143
## -4.772706e-01 -1.595434e-01 4.191378e-01 -2.708711e-01 -5.999573e-01
## 144 145 146 147 148
## 5.191558e-01 4.535474e-01 5.996607e-03 -9.373734e-04 -1.311674e-01
## 149 150 151 152 153
## -2.715960e-01 8.935407e-01 -3.683710e-02 -6.806805e-01 -2.365659e-01
## 154 155 156 157 158
## 3.931969e-01 -2.904746e-01 -2.323936e-01 -1.949843e-01 3.921652e-01
## 159 160 161 162 163
## 1.751432e-01 -4.108737e-01 3.422875e-01 4.240908e-01 2.947040e-01
## 164 165 166 167 168
## 1.910702e-01 -3.073656e-01 -2.204561e-01 -1.622853e-01 4.157310e-01
## 169 170 171 172 173
## -5.628103e-01 -5.950774e-01 -4.442669e-01 4.268981e-01 -8.790413e-02
## 174 175 176 177 178
## -7.760961e-01 3.822863e-01 2.410385e-01 -2.177960e-01 7.856436e-03
## 179 180 181 182 183
## -3.516450e-01 8.835614e-01 2.373113e-01 1.152154e-01 -4.077946e-01
## 184 185 186 187 188
## 1.237408e-01 -2.551678e-01 1.452853e-01 4.536800e-01 5.372786e-01
## 189 190 191 192 193
## 5.576472e-01 2.434842e-01 -2.687440e-01 2.015559e-01 -1.731056e-01
## 194 195 196 197 198
## 1.859901e-02 1.327086e-01 8.714665e-03 7.597549e-01 -9.719030e-02
## 199 200 201 202 203
## 1.777937e-01 1.753121e-01 1.634210e-01 3.103756e-01 1.962344e-01
## 204 205 206 207 208
## 2.355720e-01 2.579447e-02 -1.101483e-01 1.957471e-01 1.295667e-01
## 209 210 211 212 213
## 9.326177e-03 1.921895e-01 2.250625e-01 1.095405e-02 -1.748162e-01
## 214 215 216 217 218
## -4.860877e-02 1.505003e-01 -2.246712e-02 -1.416807e-01 1.745139e-01
## 219 220 221 222 223
## 3.175889e-03 5.633965e-02 1.416178e-01 9.650440e-02 1.124607e-01
## 224 225 226 227 228
## -2.674600e-01 -2.975700e-03 -4.083925e-02 1.202068e-01 6.441830e-02
## 229 230 231 232 233
## 1.599225e-01 1.702530e-01 4.276334e-02 1.619046e-01 1.660944e-01
## 234 235 236 237 238
## -1.505866e-01 -1.262807e-01 -5.238170e-02 1.587515e-01 -4.858967e-02
## 239 240 241 242 243
## -7.101033e-02 1.533114e-01 -1.020966e-01 -2.647150e-01 7.118711e-02
## 244 245 246 247 248
## -1.746871e-02 -8.212377e-02 2.090634e-02 -8.762507e-01 5.272292e-01
## 249 250 251 252 253
## 1.771021e-01 1.944207e-01 8.770354e-02 9.505982e-02 -1.673955e-01
## 254 255 256 257 258
## 1.288901e-01 -1.698953e-01 -2.957430e-01 -1.190650e-02 6.940479e-02
## 259 260 261 262 263
## -1.256510e-01 -1.967484e-01 2.719455e-02 -1.120842e-01 -2.413502e-01
## 264 265 266 267 268
## 9.046668e-02 -1.237778e-01 -2.077808e-02 -3.022515e-01 1.358665e-01
## 269 270 271 272 273
## -2.315067e-01 3.846026e-01 -6.256331e-02 1.496557e-01 -1.655589e-01
## 274 275 276 277 278
## -2.937391e-01 2.144330e-02 -6.932071e-02 -4.072256e-01 -6.913784e-02
## 279 280 281 282 283
## 8.298331e-02 -2.679270e-01 -2.504043e-03 2.889684e-02 -1.133434e-01
## 284 285 286 287 288
## 6.947883e-02 -1.471743e-01 1.864245e-01 5.975837e-02 -1.414465e-01
## 289 290 291 292 293
## -1.663160e-01 -3.660933e-01 -1.321922e-01 -1.188109e+00 -2.791208e-01
## 294 295 296 297 298
## 6.854606e-01 5.741734e-01 -5.503088e-04 1.085782e-01 2.745158e-01
## 299 300 301 302 303
## -3.659694e-01 1.154215e-01 2.014748e-01 -1.687743e-01 7.009330e-02
## 304 305 306 307 308
## -1.790854e-02 -5.183298e-01 1.614229e-01 -1.051765e-01 2.348463e-01
## 309 310 311 312 313
## 3.757950e-02 1.259562e-01 -2.366409e-01 4.863608e-04 -4.600879e-02
## 314 315 316 317 318
## 1.243534e-01 9.245526e-02 2.990036e-01 -1.568415e-01 2.043733e-01
## 319 320 321 322 323
## -1.871971e-02 7.720671e-02 -8.869464e-02 1.295716e-01 -4.715174e-02
## 324 325 326 327 328
## -1.478601e-01 1.942765e-01 -4.834625e-02 -4.917373e-01 2.841493e-01
## 329 330 331 332 333
## 7.934580e-01 3.316665e-02 3.080243e-01 -9.582168e-02 2.671148e-01
## 334 335 336 337 338
## -5.068043e-02 4.109623e-01 -1.202856e-01 -1.374851e-01 5.283613e-02
## 339 340 341 342 343
## -1.393160e-01 -1.524689e-02 -1.045450e-01 1.297566e-01 1.024932e-01
## 344 345 346 347 348
## -2.708716e-02 3.712759e-01 2.733485e-02 2.673658e-01 2.252898e-01
## 349 350 351 352 353
## 3.598315e-01 1.802376e-01 2.767110e-01 1.843797e-01 3.751562e-01
## 354 355 356 357 358
## 3.924934e-01 3.948218e-01 -6.616482e-03 -6.871730e-01 7.818524e-01
## 359 360 361 362 363
## 6.263925e-01 6.146656e-01 4.405028e-01 4.513664e-01 -8.045035e-02
## 364 365 366 367 368
## -3.001169e-01 2.543205e-01 3.740193e-01 2.972932e-01 3.435671e-01
## 369 370 371 372 373
## 3.372868e-02 -4.622732e-02 -2.679329e-01 -2.837823e-01 3.340631e-01
## 374 375 376 377 378
## 1.160161e-02 8.812509e-02 9.378014e-02 9.290555e-02 -2.734476e-01
## 379 380 381 382 383
## -1.783797e+00 2.354539e-01 5.548661e-01 4.596101e-01 3.055552e-01
## 384 385 386 387 388
## -1.314264e-01 -4.278442e-01 -3.798545e-02 2.477004e-02 -1.090278e-01
## 389 390 391 392 393
## -7.210254e-02 -8.451534e-02 -1.464771e-01 -3.089769e-01 -8.065425e-02
## 394 395 396 397 398
## 1.664003e-01 -2.551375e-01 7.743199e-02 -1.560038e-01 5.958107e-02
## 399 400 401 402 403
## -3.158753e-01 -1.857114e-01 1.754412e-01 -1.150685e-01 -2.463172e-02
## 404 405 406 407 408
## 7.116496e-03 9.622965e-03 -1.892348e-01 -5.970879e-01 1.088046e-01
## 409 410 411 412 413
## -3.529074e-01 -2.162829e-01 -1.229156e-01 -1.825564e-02 -3.704000e-02
## 414 415 416 417 418
## 8.238300e-02 -1.213248e-01 -1.790385e-02 -3.361080e-01 -1.721888e-01
## 419 420 421 422 423
## 4.501606e-01 -6.666377e-01 -9.880836e-01 1.987011e-01 -4.305947e-01
## 424 425 426 427 428
## -2.136326e-01 4.687347e-02 -3.891859e-01 -5.504740e-01 6.857461e-01
## 429 430 431 432 433
## -4.906559e-01 -2.077706e-01 -3.272321e-01 -7.705121e-01 1.902980e-01
## 434 435 436 437 438
## 1.156489e-01 -1.802610e-01 -3.750868e-01 -2.266351e-02 8.801317e-01
## 439 440 441 442 443
## -2.729067e-01 4.631069e-02 -3.079193e-01 1.982456e-01 1.451072e-01
## 444 445 446 447 448
## -2.874215e-01 1.725205e-01 1.944864e-01 -2.601933e-01 -4.456659e-01
## 449 450 451 452 453
## 4.819925e-01 -6.545991e-01 1.134555e+00 1.016110e-01 -1.077424e-02
## 454 455 456 457 458
## -4.111305e-01 6.553535e-03 -2.531074e-02 1.692089e-01 -3.413132e-02
## 459 460 461 462 463
## 2.327285e-01 2.771341e-01 -1.470341e-01 -5.716407e-01 4.615979e-01
## 464 465 466 467 468
## 4.827980e-01 2.222693e-01 3.113167e-01 3.816857e-01 -3.726330e-01
## 469 470 471 472 473
## -1.242595e-03 -7.860091e-01 4.189513e-01 1.261510e-01 4.027773e-02
## 474 475 476 477 478
## 2.257368e-01 -1.861743e-01 -3.226268e-01 3.436967e-02 5.145833e-01
## 479 480 481 482 483
## -3.705241e-02 2.356560e-01 -5.891424e-02 -2.200512e-02 5.080037e-02
## 484 485 486 487 488
## 1.972367e-02 1.825073e-01 -1.186804e-02 1.747943e-01 6.280529e-02
## 489 490
## 4.042257e-03 1.620899e-01
mod_ardl113_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,
p=13,q=1)
f_ardl113_meck <- forecast(mod_ardl113_meck ,
x= t(full_cases_wastewater_weather_data_meck_test[,8]),
h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl113_meck$forecasts)
## [1] 0.2036014
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl113_meck$forecasts)
## [1] 0.1740159
checkresiduals(mod_ardl113_meck)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## -0.0674636102 0.0860300127 0.0262707244 -0.0927458274 -0.0712622528
## 19 20 21 22 23
## 0.0888639880 0.2807548902 -0.0003207917 -0.0417452450 -0.1006078488
## 24 25 26 27 28
## 0.3189435585 0.0092949894 -0.2308598513 0.0911981481 0.3131976662
## 29 30 31 32 33
## -0.0211669333 0.0342510646 0.0812954738 -0.1124101803 0.0309032328
## 34 35 36 37 38
## -0.2758549460 0.5008353835 -0.0333697667 -0.1656519015 -0.0731238769
## 39 40 41 42 43
## -0.2159883322 0.1906916777 0.0946876931 -0.2275679945 -0.1525371097
## 44 45 46 47 48
## 0.1300018414 -0.1147138365 -0.2589956260 0.1899850354 -0.3161668179
## 49 50 51 52 53
## 0.3867053934 -0.3345783381 -0.4369526860 0.2845604542 -0.0982301679
## 54 55 56 57 58
## -0.0576858931 -0.0343592112 -0.2016265071 0.3873933567 -0.4521257496
## 59 60 61 62 63
## 0.2030932678 -0.9996957016 -0.0834241173 0.4064736940 -0.6739386362
## 64 65 66 67 68
## 0.6500515278 0.2888967988 -0.1401042846 0.2437635033 0.3409057812
## 69 70 71 72 73
## 0.4372752538 0.4289103559 0.0699742487 0.1004894884 0.0385128060
## 74 75 76 77 78
## 0.3975788961 0.1445510860 0.4359685597 0.3961884747 0.1572905511
## 79 80 81 82 83
## -0.0688584248 0.0548405362 -0.0668721173 -0.3008902113 0.1551767082
## 84 85 86 87 88
## 0.0535327937 0.3137796690 -0.3563597833 0.3774734697 -0.0867984975
## 89 90 91 92 93
## 0.1422926133 -0.2301917063 0.0019893906 0.1178041550 -0.3152019523
## 94 95 96 97 98
## 0.1480502728 -0.0806682721 0.1346760781 -0.0075596558 -0.0467269548
## 99 100 101 102 103
## -0.0432559827 -0.0076412169 0.2168196555 -0.0567160085 -0.3390908528
## 104 105 106 107 108
## 0.4790871697 -0.5897972807 0.7242023645 -0.1390918266 -0.2205401444
## 109 110 111 112 113
## 0.2744621879 -0.2952138407 0.2346255303 0.3885728086 -0.2168426934
## 114 115 116 117 118
## 0.0704215965 -0.0577900675 -0.3424600300 0.5449024645 -0.4414096317
## 119 120 121 122 123
## 0.0139634066 -0.0911158315 0.0551179001 -0.2101234170 0.0432997754
## 124 125 126 127 128
## -0.4371741068 0.0670427222 0.2097003890 -0.4177036369 -0.5744809105
## 129 130 131 132 133
## 0.0003815003 -0.5590158326 0.3015835614 -0.0034151699 0.6444188985
## 134 135 136 137 138
## -0.1383251730 -0.0833493809 -0.2407875956 -0.1915845655 0.4579679402
## 139 140 141 142 143
## -0.5208660560 0.0105941921 0.4635803451 -0.3892899737 -0.5563893241
## 144 145 146 147 148
## 0.7413985628 0.2115761590 -0.1280963925 0.0360934534 -0.0845427242
## 149 150 151 152 153
## -0.1609383244 1.1769061139 -0.1982543588 -0.7362030298 0.0370950022
## 154 155 156 157 158
## 0.5195711821 -0.2564535584 -0.2508094121 -0.0089752939 0.2431248335
## 159 160 161 162 163
## 0.0598015411 -0.5597420171 0.3868125587 0.1882599644 0.1885316633
## 164 165 166 167 168
## 0.0716024647 -0.3930704232 -0.1934066136 -0.0066910866 0.4614248324
## 169 170 171 172 173
## -0.7131701187 -0.4709956717 -0.2870384853 0.5291480422 -0.3242413530
## 174 175 176 177 178
## -0.8298340449 0.4041531154 0.1276304965 -0.5429039118 -0.0354837656
## 179 180 181 182 183
## -0.3988197884 0.8453070169 -0.1335015813 -0.1538693089 -0.4670536196
## 184 185 186 187 188
## 0.1877092442 -0.2225580888 0.1971184331 0.3783298021 0.2219334015
## 189 190 191 192 193
## 0.2932752862 0.0331670835 -0.3470463393 0.3895564001 -0.1520519119
## 194 195 196 197 198
## 0.0915174536 0.1641764478 -0.0879766841 0.7055198031 -0.3422502154
## 199 200 201 202 203
## 0.1080211959 0.1811488507 0.1308019353 0.2672395797 0.1288288761
## 204 205 206 207 208
## 0.1382744024 -0.0531464969 -0.0817146247 0.2766920211 0.1733842202
## 209 210 211 212 213
## -0.0343331014 0.2132885591 0.1613767327 -0.0832999938 -0.2002098641
## 214 215 216 217 218
## 0.0013564061 0.1975033876 -0.0618602077 -0.1907173741 0.2085062466
## 219 220 221 222 223
## -0.0897268813 -0.0177740865 0.1848667304 0.0297133968 0.0364977979
## 224 225 226 227 228
## -0.2450449156 0.0562471803 0.0220350244 0.1721302586 0.0138078142
## 229 230 231 232 233
## 0.1464700409 0.1414996760 0.0171849435 0.1879138912 0.1723378711
## 234 235 236 237 238
## -0.2211668633 -0.0320712329 0.0535356726 0.2494976844 -0.0888111498
## 239 240 241 242 243
## -0.0374485099 0.1841046900 -0.1370826122 -0.2320307746 0.1751057456
## 244 245 246 247 248
## -0.0542607240 -0.1318471226 0.0301580398 -0.9338811605 0.7284126228
## 249 250 251 252 253
## 0.0452817700 -0.0630658937 -0.0541508147 -0.0208232305 -0.2441711683
## 254 255 256 257 258
## 0.1840758702 -0.2007153448 -0.3023033572 0.0469424852 0.0614292807
## 259 260 261 262 263
## -0.2256322917 -0.2097515374 0.0448562077 -0.1447953529 -0.2729797870
## 264 265 266 267 268
## 0.1529049706 -0.2221107797 -0.0350825744 -0.3195097615 0.1780991396
## 269 270 271 272 273
## -0.3017291283 0.4019499964 -0.1816576246 0.0818792616 -0.2094871128
## 274 275 276 277 278
## -0.2900234763 0.1307775203 -0.0403513956 -0.4708812581 0.0144410942
## 279 280 281 282 283
## 0.0770736744 -0.3412619609 0.0397136665 0.0302622391 -0.2344633746
## 284 285 286 287 288
## 0.1300016531 -0.1789750776 0.2057587317 0.0226660883 -0.1989084291
## 289 290 291 292 293
## -0.1120684412 -0.2397412151 -0.0392782358 -1.1099331151 0.0277465813
## 294 295 296 297 298
## 0.8134468042 0.1801553697 -0.4028874718 -0.0417753098 0.1777225426
## 299 300 301 302 303
## -0.4578844002 0.2797611481 0.2498422899 -0.3225890380 0.0973239160
## 304 305 306 307 308
## -0.0563959808 -0.5523187547 0.2775997568 -0.0728091678 0.1088573191
## 309 310 311 312 313
## -0.0143079123 0.0303605212 -0.2887662330 0.0850970535 -0.0329067302
## 314 315 316 317 318
## 0.0558424978 0.0714429960 0.2151174047 -0.2604565525 0.2927277071
## 319 320 321 322 323
## -0.0290093266 0.1033548556 -0.0557923009 0.2113095567 -0.0468579559
## 324 325 326 327 328
## -0.1037707187 0.3031576267 -0.0347421226 -0.4438926379 0.5354343401
## 329 330 331 332 333
## 0.8244056676 -0.2278170437 0.3064034411 -0.0950029865 0.3187677278
## 334 335 336 337 338
## 0.0364553992 0.5541284401 -0.2263816130 -0.0960241921 0.1735656633
## 339 340 341 342 343
## -0.1063674980 0.0007322949 -0.0836698713 0.0646073257 0.0468320615
## 344 345 346 347 348
## -0.0699086951 0.3492374117 -0.1399546655 0.2583635682 0.1635487302
## 349 350 351 352 353
## 0.2713485365 0.0947551267 0.2384196113 0.1607348651 0.4255646122
## 354 355 356 357 358
## 0.3234367625 0.3702992447 -0.0538621146 -0.5542460192 1.1612520366
## 359 360 361 362 363
## 0.6084843173 0.3741997602 0.3947697096 0.4210373576 -0.0069876449
## 364 365 366 367 368
## 0.0192161058 0.7048840448 0.5325366145 0.2638445158 0.3602227968
## 369 370 371 372 373
## 0.0073274245 0.0700647788 -0.1410292801 0.0012790709 0.5275607978
## 374 375 376 377 378
## -0.0807730962 0.1346814747 0.0464244512 -0.0141956828 -0.1709396754
## 379 380 381 382 383
## -1.6563794992 0.8131357271 0.7228473266 0.0689225947 0.0650020037
## 384 385 386 387 388
## -0.3095189300 -0.4470566349 0.2430711576 0.2046711042 -0.1559507123
## 389 390 391 392 393
## -0.0704081443 -0.1039765620 -0.1420811383 -0.2142016806 0.0439716024
## 394 395 396 397 398
## 0.2004573841 -0.3017913120 0.1466495081 -0.1248291692 0.0829192272
## 399 400 401 402 403
## -0.2029540430 -0.0880782667 0.3315544452 -0.0733011158 0.0748198866
## 404 405 406 407 408
## 0.1501675219 0.1106979804 -0.0703802965 -0.4734525118 0.4095880969
## 409 410 411 412 413
## -0.2157052210 -0.1303159789 0.0916831527 0.0650420951 -0.0104793383
## 414 415 416 417 418
## 0.1067086492 -0.1129985972 0.0395042732 -0.1965903626 0.0430635648
## 419 420 421 422 423
## 0.6149905011 -0.7140454885 -0.8736326222 0.6371071150 -0.3903998230
## 424 425 426 427 428
## -0.2519660828 0.2110009044 -0.4920854058 -0.5576390325 0.8774120716
## 429 430 431 432 433
## -0.7435744381 -0.3974246070 -0.2020093474 -0.8414679683 0.3659963034
## 434 435 436 437 438
## 0.0118324166 -0.4513501089 -0.5131203030 0.0295041091 0.8129727078
## 439 440 441 442 443
## -0.6287802858 -0.0929971713 -0.3083509108 0.1082324515 0.0988055485
## 444 445 446 447 448
## -0.3690935817 0.0660488377 0.1173975067 -0.4038086491 -0.4343779701
## 449 450 451 452 453
## 0.5969329346 -0.8859259106 1.0548088933 -0.1794915303 -0.3698129740
## 454 455 456 457 458
## -0.3768637563 0.0955181210 -0.0046434564 0.0878533483 -0.1332838731
## 459 460 461 462 463
## 0.0628778669 0.1489849237 -0.3798635980 -0.5143970495 0.5848923495
## 464 465 466 467 468
## 0.3394519417 -0.0728864082 0.1512234649 0.1860736199 -0.5618374466
## 469 470 471 472 473
## 0.0670099122 -0.7581023064 0.5528533862 -0.0874287966 -0.2056913222
## 474 475 476 477 478
## 0.0485617082 -0.4205897296 -0.3662484912 0.0624868292 0.3533179509
## 479 480 481 482 483
## -0.3642189220 0.0867524525 -0.2139411986 -0.0977374620 0.0211438736
## 484 485 486 487 488
## -0.0390661485 0.0663988680 -0.1460124344 0.0376205601 -0.0604986558
## 489 490
## -0.1240688686 0.1094587792
mod_ardl92_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,
p=2,q=9)
summary(mod_ardl92_meck)
##
## Time series regression with "ts" data:
## Start = 10, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.76298 -0.16215 0.00894 0.17265 1.09150
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.740370 0.335063 -2.210 0.027613 *
## log_viral_gene.t -0.053319 0.035170 -1.516 0.130193
## log_viral_gene.1 0.099892 0.045907 2.176 0.030057 *
## log_viral_gene.2 0.003063 0.035356 0.087 0.931002
## log_mean_new_cases.1 0.514385 0.046179 11.139 < 2e-16 ***
## log_mean_new_cases.2 0.072966 0.051631 1.413 0.158259
## log_mean_new_cases.3 0.181462 0.051536 3.521 0.000472 ***
## log_mean_new_cases.4 0.081804 0.052151 1.569 0.117418
## log_mean_new_cases.5 0.109375 0.051967 2.105 0.035851 *
## log_mean_new_cases.6 0.074401 0.052030 1.430 0.153396
## log_mean_new_cases.7 -0.006672 0.051322 -0.130 0.896621
## log_mean_new_cases.8 0.003192 0.051478 0.062 0.950588
## log_mean_new_cases.9 -0.103250 0.045770 -2.256 0.024542 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3133 on 468 degrees of freedom
## Multiple R-squared: 0.9217, Adjusted R-squared: 0.9197
## F-statistic: 458.9 on 12 and 468 DF, p-value: < 2.2e-16
f_ardl92_meck <- forecast(mod_ardl92_meck ,
x= t(full_cases_wastewater_weather_data_meck_test[,8]),
h=14, interval = TRUE)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl92_meck$forecasts[,2])
## [1] 0.1207945
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl92_meck$forecasts[,2])
## [1] 0.09736353
checkresiduals(mod_ardl92_meck)
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -3.092371e-02 1.163238e-02 1.252001e-02 1.014782e-01 2.836953e-02
## 15 16 17 18 19
## 2.833400e-02 -1.696518e-03 -1.227269e-01 -1.590525e-01 -3.045078e-02
## 20 21 22 23 24
## 2.184542e-01 5.078416e-02 -3.255922e-02 -1.214547e-01 2.311235e-01
## 25 26 27 28 29
## 4.023654e-02 -2.353277e-01 -8.977339e-02 1.961115e-01 5.112010e-03
## 30 31 32 33 34
## -3.149867e-02 1.427563e-02 -2.207462e-01 -2.851758e-02 -2.929289e-01
## 35 36 37 38 39
## 3.177582e-01 4.487638e-02 -9.499900e-02 -8.387231e-02 -2.265090e-01
## 40 41 42 43 44
## 8.259352e-02 9.959311e-02 -8.641751e-02 -1.764461e-01 1.229113e-01
## 45 46 47 48 49
## -7.265117e-02 -2.519822e-01 9.349147e-02 -2.707908e-01 3.195785e-01
## 50 51 52 53 54
## -2.050264e-01 -3.964405e-01 1.363230e-01 1.925282e-02 2.139667e-02
## 55 56 57 58 59
## -1.014455e-01 -1.146824e-01 3.385559e-01 -3.207601e-01 1.507240e-01
## 60 61 62 63 64
## -1.071141e+00 -2.682274e-01 2.178915e-01 -5.722560e-01 6.045407e-01
## 65 66 67 68 69
## 3.489794e-01 2.040119e-01 -3.519632e-02 2.839743e-01 2.117074e-01
## 70 71 72 73 74
## 3.177930e-01 -4.062772e-02 -6.585365e-02 -2.198761e-01 4.218497e-01
## 75 76 77 78 79
## -1.655438e-01 4.272526e-01 3.326260e-01 3.096256e-01 -1.568450e-02
## 80 81 82 83 84
## -6.525427e-02 -1.434785e-01 -3.334671e-01 -2.611591e-02 -4.666716e-02
## 85 86 87 88 89
## 3.474433e-01 -2.150304e-01 3.881112e-01 2.499551e-02 2.028181e-01
## 90 91 92 93 94
## -2.367724e-01 -8.491285e-02 1.206571e-02 -3.959261e-01 3.882358e-02
## 95 96 97 98 99
## -2.155568e-01 1.809715e-01 8.645893e-02 2.824313e-03 -1.786669e-02
## 100 101 102 103 104
## -8.591058e-02 2.274223e-01 -1.068923e-01 -3.708266e-01 3.465886e-01
## 105 106 107 108 109
## -4.702015e-01 6.073526e-01 -6.934208e-02 -1.380305e-01 1.090499e-01
## 110 111 112 113 114
## -3.081340e-01 9.294370e-02 2.802856e-01 -1.150670e-01 -4.287394e-02
## 115 116 117 118 119
## -1.069286e-01 -4.091438e-01 3.187158e-01 -3.036462e-01 -8.434482e-02
## 120 121 122 123 124
## -1.245349e-01 4.561678e-02 -1.409853e-01 -2.357035e-02 -3.462645e-01
## 125 126 127 128 129
## -4.734365e-03 3.363099e-01 -2.809807e-01 -6.658337e-01 -1.931057e-01
## 130 131 132 133 134
## -8.923531e-01 9.462148e-02 -1.521770e-01 7.699534e-01 7.831224e-02
## 135 136 137 138 139
## 1.447998e-01 -2.591512e-01 -2.804563e-01 1.452160e-01 -5.340732e-01
## 140 141 142 143 144
## -1.774752e-01 3.831458e-01 -2.355669e-01 -5.379080e-01 4.430436e-01
## 145 146 147 148 149
## 4.268551e-01 7.313508e-02 8.329347e-02 -2.276817e-01 -3.157568e-01
## 150 151 152 153 154
## 9.449980e-01 -1.127343e-02 -7.474956e-01 -3.350319e-01 6.629206e-01
## 155 156 157 158 159
## -3.926999e-01 -2.283320e-01 -2.171595e-01 3.702117e-01 2.552329e-01
## 160 161 162 163 164
## -3.746085e-01 3.234608e-01 3.548603e-01 3.353210e-01 1.897544e-01
## 165 166 167 168 169
## -3.546162e-01 -2.689742e-01 -1.656706e-01 3.926646e-01 -5.638034e-01
## 170 171 172 173 174
## -6.236650e-01 -3.644881e-01 2.419904e-01 6.867030e-02 -7.785484e-01
## 175 176 177 178 179
## 3.596520e-01 2.556221e-01 -2.183095e-01 5.990763e-02 -4.009686e-01
## 180 181 182 183 184
## 9.059714e-01 2.544917e-01 1.393752e-01 -4.475876e-01 5.457393e-02
## 185 186 187 188 189
## -2.374567e-01 8.340786e-02 4.492369e-01 4.403853e-01 5.910953e-01
## 190 191 192 193 194
## 2.577866e-01 -1.954837e-01 1.473030e-01 -1.985440e-01 -4.717432e-02
## 195 196 197 198 199
## 7.214516e-02 -1.357494e-02 7.170069e-01 -1.940442e-02 1.830457e-01
## 200 201 202 203 204
## 1.607166e-01 1.394537e-01 2.803610e-01 1.726479e-01 1.823049e-01
## 205 206 207 208 209
## 3.561684e-02 -9.836023e-02 1.927115e-01 6.261834e-02 -1.391065e-02
## 210 211 212 213 214
## 1.735067e-01 1.859842e-01 7.134149e-02 -1.744462e-01 -5.452612e-02
## 215 216 217 218 219
## 1.558357e-01 -3.467078e-02 -1.510130e-01 1.601537e-01 -2.934839e-02
## 220 221 222 223 224
## 5.364477e-02 1.838195e-01 3.012772e-02 9.895059e-02 -2.495102e-01
## 225 226 227 228 229
## -1.737132e-02 -1.475369e-02 1.207811e-01 8.583218e-02 1.213871e-01
## 230 231 232 233 234
## 1.855354e-01 4.753981e-02 1.866039e-01 1.354519e-01 -1.621541e-01
## 235 236 237 238 239
## -1.476087e-01 -9.523335e-03 1.469191e-01 -5.875478e-02 -6.073574e-02
## 240 241 242 243 244
## 1.394707e-01 -9.513615e-02 -2.445320e-01 8.757945e-02 -2.934725e-02
## 245 246 247 248 249
## -9.233432e-02 2.892464e-02 -8.366786e-01 5.078695e-01 2.107009e-01
## 250 251 252 253 254
## 2.047745e-01 8.030800e-02 1.051612e-01 -1.453955e-01 9.064731e-02
## 255 256 257 258 259
## -1.313186e-01 -4.096315e-01 -1.006922e-02 7.446587e-02 -1.236577e-01
## 260 261 262 263 264
## -1.928842e-01 6.074715e-02 -1.290528e-01 -2.034470e-01 7.606261e-02
## 265 266 267 268 269
## -1.389784e-01 -2.766717e-02 -2.661200e-01 1.163460e-01 -2.396346e-01
## 270 271 272 273 274
## 4.097262e-01 -4.466364e-02 1.329093e-01 -1.376155e-01 -3.050477e-01
## 275 276 277 278 279
## 6.348342e-02 -1.009835e-01 -3.900220e-01 -1.174700e-01 1.093365e-01
## 280 281 282 283 284
## -2.734615e-01 4.514930e-02 -1.382426e-02 -1.349219e-01 1.037062e-01
## 285 286 287 288 289
## -1.236246e-01 1.722392e-01 6.008186e-02 -1.184771e-01 -1.498106e-01
## 290 291 292 293 294
## -3.679851e-01 -1.146621e-01 -1.211610e+00 -2.829368e-01 6.819258e-01
## 295 296 297 298 299
## 5.833887e-01 5.790571e-02 1.464892e-01 3.321741e-01 -3.720783e-01
## 300 301 302 303 304
## 1.564222e-01 1.168640e-01 -2.581056e-01 1.968431e-02 2.939600e-02
## 305 306 307 308 309
## -5.594626e-01 2.314759e-01 -7.625572e-02 1.770047e-01 6.695224e-02
## 310 311 312 313 314
## 1.017863e-01 -2.388097e-01 2.251281e-03 -3.007638e-02 6.243413e-02
## 315 316 317 318 319
## 1.010172e-01 2.798638e-01 -1.123650e-01 1.994614e-01 2.516946e-02
## 320 321 322 323 324
## 1.304755e-02 -9.812070e-02 1.101769e-01 -5.688409e-02 -1.611528e-01
## 325 326 327 328 329
## 2.100385e-01 -4.400001e-02 -5.062325e-01 2.867265e-01 8.064437e-01
## 330 331 332 333 334
## 3.036679e-02 3.228944e-01 -6.375375e-02 2.207628e-01 3.847121e-02
## 335 336 337 338 339
## 4.157262e-01 -1.862650e-01 -2.152798e-01 1.450628e-01 -1.573700e-01
## 340 341 342 343 344
## -3.183065e-02 -9.206769e-02 1.181346e-01 7.614366e-02 2.500905e-02
## 345 346 347 348 349
## 3.277367e-01 7.651524e-03 2.772196e-01 2.234536e-01 3.496113e-01
## 350 351 352 353 354
## 1.703349e-01 2.441747e-01 2.443558e-01 3.307703e-01 4.035216e-01
## 355 356 357 358 359
## 3.452711e-01 -2.891394e-02 -7.149718e-01 7.580044e-01 6.009496e-01
## 360 361 362 363 364
## 5.801873e-01 4.424346e-01 4.607344e-01 -7.361956e-02 -2.887587e-01
## 365 366 367 368 369
## 2.649712e-01 2.405537e-01 2.796954e-01 2.958525e-01 2.132516e-01
## 370 371 372 373 374
## -2.750058e-02 -2.824429e-01 -1.764350e-01 2.016469e-01 -1.351666e-02
## 375 376 377 378 379
## 1.020631e-01 6.526443e-02 1.155335e-01 -2.553103e-01 -1.762980e+00
## 380 381 382 383 384
## 2.101670e-01 5.359992e-01 4.782681e-01 3.562092e-01 -8.033185e-02
## 385 386 387 388 389
## -3.883561e-01 2.627346e-02 7.952609e-02 -2.607643e-01 -1.175277e-01
## 390 391 392 393 394
## -5.857509e-02 -1.150789e-01 -2.598925e-01 -4.213645e-02 1.198930e-01
## 395 396 397 398 399
## -2.661433e-01 1.489386e-01 -2.024840e-01 7.704819e-02 -2.903232e-01
## 400 401 402 403 404
## -1.647626e-01 1.643158e-01 -1.258556e-01 7.388809e-02 -7.547620e-02
## 405 406 407 408 409
## 4.738201e-02 -1.695564e-01 -5.873658e-01 1.816129e-01 -3.658345e-01
## 410 411 412 413 414
## -1.541965e-01 -1.419844e-01 8.592332e-03 -7.089878e-03 1.165630e-01
## 415 416 417 418 419
## -6.272235e-02 -5.778883e-02 -2.247626e-01 -2.778469e-01 4.572784e-01
## 420 421 422 423 424
## -6.440206e-01 -1.030302e+00 3.249665e-01 -4.085808e-01 -1.785736e-01
## 425 426 427 428 429
## 7.035872e-02 -3.651298e-01 -5.662069e-01 7.933071e-01 -4.768814e-01
## 430 431 432 433 434
## -2.922878e-01 -2.685913e-01 -7.243048e-01 1.725235e-01 1.543828e-01
## 435 436 437 438 439
## -1.620727e-01 -4.584507e-01 5.191641e-02 9.345671e-01 -3.536851e-01
## 440 441 442 443 444
## 6.352328e-02 -3.436279e-01 1.305824e-01 2.842651e-01 -3.008418e-01
## 445 446 447 448 449
## 1.386451e-01 1.215209e-01 -2.017925e-01 -4.699615e-01 4.751846e-01
## 450 451 452 453 454
## -7.258056e-01 1.091502e+00 1.442230e-01 -1.525797e-02 -4.045037e-01
## 455 456 457 458 459
## 1.532905e-02 -3.790277e-02 8.403449e-02 -3.366523e-02 2.058621e-01
## 460 461 462 463 464
## 2.752573e-01 -1.232036e-01 -5.652366e-01 4.062207e-01 4.750853e-01
## 465 466 467 468 469
## 1.755680e-01 3.300130e-01 3.608029e-01 -3.666815e-01 -5.185949e-02
## 470 471 472 473 474
## -6.779433e-01 3.216355e-01 7.937263e-02 5.339369e-02 1.819193e-01
## 475 476 477 478 479
## -1.874273e-01 -3.059841e-01 8.937394e-03 4.802756e-01 -1.195863e-01
## 480 481 482 483 484
## 2.334788e-01 -2.064050e-02 -4.314131e-02 6.413132e-02 -4.859655e-03
## 485 486 487 488 489
## 1.579740e-01 -5.826499e-02 1.890077e-01 6.867093e-02 -4.940313e-05
## 490
## 1.385353e-01
exp(f_ardl92_meck $forecasts[1,2])
## [1] 3.694923
exp(f_ardl92_meck $forecasts[1,1])
## [1] 1.990954
exp(f_ardl92_meck $forecasts[1,3])
## [1] 6.8191
exp(f_ardl92_meck $forecasts[1,2]) - exp(full_cases_wastewater_weather_data_meck_test[1,7])
## [1] 0.668796
exp(f_ardl92_meck $forecasts[7,2])
## [1] 3.803504
exp(f_ardl92_meck $forecasts[7,1])
## [1] 1.601884
exp(f_ardl92_meck $forecasts[7,3])
## [1] 8.752501
exp(f_ardl92_meck $forecasts[7,2]) - exp(full_cases_wastewater_weather_data_meck_test[7,7])
## [1] -0.05095394
exp(f_ardl92_meck $forecasts[14,2])
## [1] 3.852675
exp(f_ardl92_meck $forecasts[14,1])
## [1] 1.268613
exp(f_ardl92_meck $forecasts[14,3])
## [1] 13.59007
exp(f_ardl92_meck $forecasts[14,2]) - exp(full_cases_wastewater_weather_data_meck_test[14,7])
## [1] 0.8327343
lowest_rmse_weather_meck <- Inf
best_mod_weather_meck <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
remove = list(p =list(TAVG=c(1:p),mean_precipation=c(1:p)))
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_meck_train,
p=p,q=q,
remove = remove)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_meck_test[,c(8,5,6)]),h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_weather_meck){
lowest_rmse_weather_meck <- forecast_acc
best_mod_weather_meck <- mod
}
}
}
lowest_rmse_weather_meck #0.118
## [1] 0.1178899
summary(best_mod_weather_meck) #ARDL(8,13)(lowest RMSE), ARDL(8,14)(lowest MAE)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.69824 -0.16711 0.00604 0.17618 1.01867
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.125372 0.478060 -0.262 0.793247
## log_viral_gene.t -0.063206 0.035437 -1.784 0.075160 .
## log_viral_gene.1 0.125407 0.046027 2.725 0.006687 **
## log_viral_gene.2 -0.050328 0.046166 -1.090 0.276229
## log_viral_gene.3 0.116435 0.046220 2.519 0.012109 *
## log_viral_gene.4 -0.111584 0.046575 -2.396 0.016990 *
## log_viral_gene.5 0.067784 0.046795 1.449 0.148160
## log_viral_gene.6 -0.068752 0.046795 -1.469 0.142468
## log_viral_gene.7 0.044782 0.046578 0.961 0.336846
## log_viral_gene.8 -0.022033 0.046471 -0.474 0.635645
## log_viral_gene.9 0.007141 0.046057 0.155 0.876852
## log_viral_gene.10 0.006222 0.045832 0.136 0.892077
## log_viral_gene.11 0.039933 0.045799 0.872 0.383719
## log_viral_gene.12 -0.059399 0.045111 -1.317 0.188601
## log_viral_gene.13 -0.030162 0.034517 -0.874 0.382681
## mean_precipation.t -0.091274 0.058839 -1.551 0.121542
## TAVG.t 0.001810 0.001145 1.581 0.114588
## log_mean_new_cases.1 0.515103 0.047083 10.940 < 2e-16 ***
## log_mean_new_cases.2 0.044340 0.052916 0.838 0.402512
## log_mean_new_cases.3 0.202523 0.052882 3.830 0.000146 ***
## log_mean_new_cases.4 0.046269 0.053482 0.865 0.387430
## log_mean_new_cases.5 0.135124 0.053921 2.506 0.012563 *
## log_mean_new_cases.6 0.061860 0.052991 1.167 0.243676
## log_mean_new_cases.7 0.004953 0.052940 0.094 0.925506
## log_mean_new_cases.8 -0.029338 0.048120 -0.610 0.542382
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3125 on 452 degrees of freedom
## Multiple R-squared: 0.9241, Adjusted R-squared: 0.9201
## F-statistic: 229.3 on 24 and 452 DF, p-value: < 2.2e-16
remove <- list(p =list(TAVG=c(1:13),mean_precipation=c(1:13)))
mod_ardl813_weather_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene +
mean_precipation +
TAVG,
data = full_cases_wastewater_weather_data_meck_train,
p=13,q=8,
remove = remove)
f_ardl813_weather_meck <- forecast(mod_ardl813_weather_meck,
x= t(full_cases_wastewater_weather_data_meck_test[,c(8,5,6)]),
h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl813_weather_meck$forecasts)
## [1] 0.1178899
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl813_weather_meck$forecasts)
## [1] 0.09683786
checkresiduals(mod_ardl813_weather_meck)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## -0.0203143239 0.0642146685 0.0221526864 -0.0962701813 -0.1417690848
## 19 20 21 22 23
## -0.0157338728 0.2341887783 0.0319256507 -0.0052776122 -0.0456536696
## 24 25 26 27 28
## 0.2605503730 0.0744736679 -0.2200575064 -0.0301138716 0.3005537191
## 29 30 31 32 33
## 0.0502998395 -0.0182677882 0.0108076095 -0.1362496950 -0.0632185773
## 34 35 36 37 38
## -0.3611747982 0.4360537756 0.0443800585 -0.0830318601 -0.1249826246
## 39 40 41 42 43
## -0.2313653802 0.1678936839 0.1490431467 -0.0997737971 -0.1034627890
## 44 45 46 47 48
## 0.2040485017 -0.0409551952 -0.1914122679 0.1739588227 -0.2433583639
## 49 50 51 52 53
## 0.4119306818 -0.1800399409 -0.3258329159 0.1656971234 -0.0269440642
## 54 55 56 57 58
## 0.0174023405 0.0570945322 -0.1232945650 0.3665669388 -0.3215899330
## 59 60 61 62 63
## 0.1705313106 -1.0076204852 -0.2970204584 0.1920336460 -0.4654790854
## 64 65 66 67 68
## 0.5966773420 0.4124931965 0.0928354364 0.1501158637 0.2192061455
## 69 70 71 72 73
## 0.3329158026 0.2723225144 -0.0163482285 0.0601135859 -0.0757139970
## 74 75 76 77 78
## 0.2047617535 0.0682958197 0.3640765833 0.3212311459 0.1721120298
## 79 80 81 82 83
## -0.1584374838 -0.1519486293 -0.2896536998 -0.4290702151 -0.1903976126
## 84 85 86 87 88
## -0.0048197007 0.3464351330 -0.2376521993 0.3583399143 0.0169329525
## 89 90 91 92 93
## 0.2159660604 -0.2381066654 -0.0613369296 -0.0092211788 -0.3701270765
## 94 95 96 97 98
## -0.0359904190 -0.1652836823 0.1084614693 -0.0002161939 0.0211436694
## 99 100 101 102 103
## -0.0591298835 -0.0540648466 0.1511041317 -0.0503977813 -0.3401795942
## 104 105 106 107 108
## 0.3362220203 -0.5849450853 0.5720154100 -0.0841694877 -0.1257906198
## 109 110 111 112 113
## 0.1472849240 -0.2908293039 0.1002674005 0.3246578791 -0.1556118761
## 114 115 116 117 118
## -0.0232181809 -0.1783368264 -0.4536467881 0.3043025317 -0.4324920378
## 119 120 121 122 123
## -0.0599007571 -0.2124356139 0.0724487815 -0.2040099066 0.0068871325
## 124 125 126 127 128
## -0.4251489233 0.0159808478 0.1693657510 -0.2771325888 -0.6149342534
## 129 130 131 132 133
## -0.2489195194 -0.6951349156 0.0378558678 -0.1040001309 0.6821632225
## 134 135 136 137 138
## 0.1007378456 0.0828216046 -0.2662099146 -0.3048662113 0.2331487310
## 139 140 141 142 143
## -0.5227913064 -0.1700500211 0.2930506640 -0.3327859785 -0.6874968738
## 144 145 146 147 148
## 0.4137984189 0.2588582952 0.0112010002 -0.0129364056 -0.1308384686
## 149 150 151 152 153
## -0.2848042777 0.9031607272 -0.0439192902 -0.6190688700 -0.3086649420
## 154 155 156 157 158
## 0.2384689007 -0.1914791623 -0.2242573370 -0.1310967675 0.2172074459
## 159 160 161 162 163
## 0.1148629572 -0.5143582486 0.2765788871 0.2269333201 0.3186197457
## 164 165 166 167 168
## 0.2095242376 -0.3321430121 -0.3050401549 -0.2157816192 0.4431785682
## 169 170 171 172 173
## -0.5847592376 -0.5584305108 -0.5088650127 0.4110744806 -0.1861459192
## 174 175 176 177 178
## -0.7199975478 0.2252349236 0.2517954784 -0.3189681924 -0.0549944957
## 179 180 181 182 183
## -0.2757485545 0.9648990680 0.2407087603 0.0831697982 -0.3769729565
## 184 185 186 187 188
## 0.1382628159 -0.2492918404 0.1696000020 0.3851359916 0.4847679801
## 189 190 191 192 193
## 0.5096161033 0.2730054054 -0.2306503505 0.2431031331 -0.1628124671
## 194 195 196 197 198
## -0.0354470449 0.0377364501 -0.0529059984 0.8359939803 -0.1237935272
## 199 200 201 202 203
## 0.1166828888 0.0761733649 0.1491359308 0.2271275329 0.1647063447
## 204 205 206 207 208
## 0.1937643184 0.0297349997 -0.1768733680 0.0876970550 0.0980910344
## 209 210 211 212 213
## -0.0567716459 0.1487311684 0.1579953238 -0.0366468213 -0.2507853419
## 214 215 216 217 218
## -0.1329910814 0.1357272398 -0.0340847439 -0.1860000523 0.1185787079
## 219 220 221 222 223
## -0.0749696700 -0.0364475867 0.1233545133 0.0562435556 0.0464463407
## 224 225 226 227 228
## -0.2277725342 0.0256302342 -0.0131479983 0.1915516828 0.0069905379
## 229 230 231 232 233
## 0.1589004130 0.1468468861 0.0609039534 0.0988501618 0.1139518272
## 234 235 236 237 238
## -0.2555130367 -0.1765469280 -0.1011533562 0.1451295796 -0.1170498461
## 239 240 241 242 243
## -0.1069472144 0.0937285546 -0.1042433936 -0.2428256709 0.0084470621
## 244 245 246 247 248
## -0.0887202380 -0.1354281689 -0.0008655397 -0.9009830281 0.5155341314
## 249 250 251 252 253
## 0.1302273662 0.1935987033 0.0364842877 0.1153657797 -0.1826642620
## 254 255 256 257 258
## 0.1166954798 -0.2152168583 -0.2977803105 -0.0490304892 0.0606004134
## 259 260 261 262 263
## -0.1525590628 -0.1978753728 0.0372361360 -0.0457467040 -0.1901918886
## 264 265 266 267 268
## 0.1060376845 -0.1454021675 0.0035783867 -0.3152010995 0.1425978952
## 269 270 271 272 273
## -0.2661500917 0.4020322085 -0.0713545879 0.1968470126 -0.1604115039
## 274 275 276 277 278
## -0.2802755530 0.0060378996 -0.0484880253 -0.4291855829 -0.0750472865
## 279 280 281 282 283
## 0.0603642707 -0.2694157213 -0.0220139788 0.0121326400 -0.1671129219
## 284 285 286 287 288
## 0.0815255705 -0.1617992175 0.2065798945 0.0945147066 -0.1007847523
## 289 290 291 292 293
## -0.1355236781 -0.2935207428 -0.1463894937 -1.2190918347 -0.3122416813
## 294 295 296 297 298
## 0.6476767936 0.5440209219 -0.0006621298 0.1384734125 0.3152930534
## 299 300 301 302 303
## -0.2814223710 0.1573515046 0.2357901423 -0.1613190481 0.0817917999
## 304 305 306 307 308
## -0.0245059674 -0.4605745667 0.1736199335 -0.0429403702 0.2105257434
## 309 310 311 312 313
## 0.0746441784 0.1449202538 -0.2215348207 0.0336543743 -0.0588420883
## 314 315 316 317 318
## 0.0596107572 0.1031129090 0.3498509593 -0.1064313038 0.2899534055
## 319 320 321 322 323
## -0.0205208657 0.1018861166 -0.0906392809 0.1761752557 -0.0465052925
## 324 325 326 327 328
## -0.1328821294 0.1842169998 -0.0432170205 -0.4770804196 0.3125547085
## 329 330 331 332 333
## 0.8188515834 0.0363209395 0.3361401139 -0.0938030912 0.2653813301
## 334 335 336 337 338
## -0.0907210149 0.4405444471 -0.1965091300 -0.1476269257 0.0022000190
## 339 340 341 342 343
## -0.0994442345 -0.0734120983 -0.1400562709 0.0203673945 0.0837196017
## 344 345 346 347 348
## 0.0061852548 0.3650879241 -0.0124002444 0.2974099695 0.1955461851
## 349 350 351 352 353
## 0.3657893799 0.2458340245 0.3719393571 0.2437855614 0.4733702273
## 354 355 356 357 358
## 0.3900479357 0.4198671850 -0.0546503866 -0.7072608675 0.7241529505
## 359 360 361 362 363
## 0.5605970772 0.5083266504 0.4049443815 0.4553483873 -0.1007641098
## 364 365 366 367 368
## -0.2922083740 0.3851627220 0.3748535489 0.2250282519 0.2944493854
## 369 370 371 372 373
## 0.0008209392 -0.0409349563 -0.3764073751 -0.2435793033 0.2704995089
## 374 375 376 377 378
## -0.0940332748 0.0850883489 -0.0355860857 -0.0496652599 -0.2423150631
## 379 380 381 382 383
## -1.6982410726 0.2147201745 0.5910289662 0.5142618292 0.3592949699
## 384 385 386 387 388
## 0.0261799756 -0.3438853076 0.0164080542 0.0618316204 -0.1035605100
## 389 390 391 392 393
## -0.0344583807 -0.0632393354 -0.1002096507 -0.2454546772 -0.0320204323
## 394 395 396 397 398
## 0.1978751642 -0.1961750837 0.1356950772 -0.1139990671 0.0841407471
## 399 400 401 402 403
## -0.2239419457 -0.1305148047 0.2403128705 -0.0561712495 0.0080853520
## 404 405 406 407 408
## 0.0354909578 0.0599148370 -0.1226677317 -0.6015776911 0.1255111531
## 409 410 411 412 413
## -0.3329367310 -0.2666023176 -0.1096017175 0.0346233057 -0.0057395080
## 414 415 416 417 418
## 0.0443203671 -0.1754897024 -0.0780696711 -0.3307083468 -0.1517845636
## 419 420 421 422 423
## 0.4567044639 -0.5710228308 -0.9909538629 0.1914160273 -0.4169079328
## 424 425 426 427 428
## -0.3053929428 0.0819314030 -0.3282032228 -0.5533628793 0.6174301855
## 429 430 431 432 433
## -0.5033940628 -0.1625260107 -0.2903992608 -0.7133682638 0.3616917890
## 434 435 436 437 438
## 0.1832756511 -0.1103716949 -0.3624778946 0.0730063877 0.9683172477
## 439 440 441 442 443
## -0.2617572985 0.0338017321 -0.2414802379 0.2411562596 0.1829585497
## 444 445 446 447 448
## -0.1895947232 0.1554974354 0.2711745745 -0.1850795987 -0.3982683933
## 449 450 451 452 453
## 0.4747383315 -0.6764453710 1.0186715030 0.0903838056 0.1060215837
## 454 455 456 457 458
## -0.3651305119 0.0647948187 0.0057320166 0.1768641626 0.1081144227
## 459 460 461 462 463
## 0.2303513065 0.2961644533 -0.1866256958 -0.4950846855 0.4418629718
## 464 465 466 467 468
## 0.4809856021 0.2157767960 0.2845607589 0.3800488446 -0.3451205740
## 469 470 471 472 473
## 0.0324299880 -0.6738465247 0.5175620400 0.0354623163 0.0692399292
## 474 475 476 477 478
## 0.1709385618 -0.2035540862 -0.3212426396 -0.0260255152 0.4063769225
## 479 480 481 482 483
## -0.0812750750 0.3082155777 -0.0068808216 0.0722527342 0.0773470752
## 484 485 486 487 488
## 0.0622704061 0.1864157543 0.0290805001 0.1879467929 0.0630865018
## 489 490
## 0.0070184936 0.1902128584
remove <- list(p =list(TAVG=c(1:14),mean_precipation=c(1:14)))
mod_ardl814_weather_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene +
mean_precipation +
TAVG,
data = full_cases_wastewater_weather_data_meck_train,
p=14,q=8,
remove = remove)
f_ardl814_weather_meck <- forecast(mod_ardl814_weather_meck,
x= t(full_cases_wastewater_weather_data_meck_test[,c(8,5,6)]),
h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl814_weather_meck$forecasts)
## [1] 0.1185831
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl814_weather_meck$forecasts)
## [1] 0.09460726
checkresiduals(mod_ardl814_weather_meck)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## 0.0236284941 0.0441732705 -0.1013308735 -0.1415546485 -0.0188112659
## 20 21 22 23 24
## 0.2342149885 0.0030395560 0.0220448667 -0.0538295688 0.2568804434
## 25 26 27 28 29
## 0.0704903957 -0.2252088926 -0.0289202885 0.3049585789 0.0520915087
## 30 31 32 33 34
## -0.0382491677 0.0128643359 -0.1372025628 -0.0664549159 -0.3567931199
## 35 36 37 38 39
## 0.4476225861 0.0497800708 -0.1005062715 -0.1270770989 -0.2315188594
## 40 41 42 43 44
## 0.1635325890 0.1477529951 -0.1325181590 -0.0946654146 0.2428031801
## 45 46 47 48 49
## -0.0417902607 -0.1964889486 0.1649116168 -0.2408897241 0.4287377655
## 50 51 52 53 54
## -0.1831911204 -0.3467905165 0.1629964958 -0.0267752040 0.0118260240
## 55 56 57 58 59
## 0.0494214356 -0.1235984436 0.3499110306 -0.3199827675 0.1682726052
## 60 61 62 63 64
## -1.0085887487 -0.2999942953 0.1997490453 -0.4318964866 0.5990048053
## 65 66 67 68 69
## 0.3815739309 0.0919405600 0.1422469696 0.2136003566 0.3302354541
## 70 71 72 73 74
## 0.2443307912 -0.0146388136 0.0635284063 -0.0879316563 0.2067473834
## 75 76 77 78 79
## 0.0594774874 0.3658710879 0.2391088805 0.1735827042 -0.1554051567
## 80 81 82 83 84
## -0.1322345524 -0.2721308779 -0.4239276762 -0.1623063923 0.1321196864
## 85 86 87 88 89
## 0.3548218837 -0.2333162531 0.3570649839 0.0158628806 0.2131095069
## 90 91 92 93 94
## -0.2362302468 -0.0514782308 0.0001655113 -0.3569912686 -0.0336831873
## 95 96 97 98 99
## -0.1651957691 0.1069405837 0.0031111717 0.0318995578 -0.0563610955
## 100 101 102 103 104
## -0.0650883051 0.1491959798 -0.0533842550 -0.3421583805 0.3376886883
## 105 106 107 108 109
## -0.6183869002 0.5842914235 -0.0382588630 -0.1300022410 0.1472675420
## 110 111 112 113 114
## -0.2939161931 0.1006226223 0.3008592344 -0.1466933100 -0.0131525750
## 115 116 117 118 119
## -0.1783547371 -0.4541350703 0.3035087539 -0.4268096464 -0.0644256607
## 120 121 122 123 124
## -0.2018956226 0.0667072564 -0.2051468384 0.0066737258 -0.4222166081
## 125 126 127 128 129
## 0.0207517385 0.1647533938 -0.2685480695 -0.5684281897 -0.2477791594
## 130 131 132 133 134
## -0.6933166002 0.0419610590 -0.1002127191 0.6599853944 0.1188468921
## 135 136 137 138 139
## 0.0808087262 -0.2801234659 -0.3104294378 0.2240874271 -0.5253082948
## 140 141 142 143 144
## -0.2378945090 0.3108061672 -0.3482106881 -0.6757198201 0.4206199928
## 145 146 147 148 149
## 0.2696302549 0.0243925865 0.0373229073 -0.1249584925 -0.2707408926
## 150 151 152 153 154
## 0.9020316796 -0.0484097728 -0.6301381852 -0.3037500687 0.1939051426
## 155 156 157 158 159
## -0.1845633041 -0.1763075348 -0.1213200304 0.1758149268 0.1179527149
## 160 161 162 163 164
## -0.5001809725 0.2918538518 0.2435255328 0.3258668327 0.3071738504
## 165 166 167 168 169
## -0.3933762130 -0.3049529355 -0.2113146384 0.4748776811 -0.5787017938
## 170 171 172 173 174
## -0.5547854749 -0.5075730040 0.4086640235 -0.1796712673 -0.7205060184
## 175 176 177 178 179
## 0.2201998398 0.2673079548 -0.3197223815 -0.0624276323 -0.2377404135
## 180 181 182 183 184
## 0.9699082138 0.2263955101 0.0092263345 -0.3163487297 0.1305194456
## 185 186 187 188 189
## -0.2540554785 0.1654559519 0.3526391356 0.4858152825 0.5139030740
## 190 191 192 193 194
## 0.3060530405 -0.2424893311 0.2350329795 -0.1709678617 -0.0567108136
## 195 196 197 198 199
## 0.0449879304 -0.0450563462 0.8330783226 -0.1258464551 0.1165182864
## 200 201 202 203 204
## 0.0813614631 0.1794064915 0.2281824148 0.1657279687 0.1975605229
## 205 206 207 208 209
## 0.0230460542 -0.1760630547 0.0929005653 0.1326454144 -0.0557525528
## 210 211 212 213 214
## 0.1499882354 0.1480563979 -0.0377810282 -0.2526197942 -0.1301589753
## 215 216 217 218 219
## 0.1774252961 -0.0360362370 -0.1841879666 0.1020190037 -0.0755621113
## 220 221 222 223 224
## -0.0368125592 0.1237322682 0.0871143151 0.0427377765 -0.2319583814
## 225 226 227 228 229
## 0.0319141591 -0.0222694121 0.1816045460 0.0013253019 0.1400025279
## 230 231 232 233 234
## 0.1446182557 0.0567527435 0.0679309681 0.1141727436 -0.2579486863
## 235 236 237 238 239
## -0.1773018223 -0.0748104964 0.1479071826 -0.1142701971 -0.1238770312
## 240 241 242 243 244
## 0.0922216719 -0.1099720780 -0.2495378726 0.0010096046 -0.0854946440
## 245 246 247 248 249
## -0.1297934119 0.0212590987 -0.9053922935 0.5109879508 0.1285605489
## 250 251 252 253 254
## 0.1836367794 0.0323123867 0.1141870341 -0.1803387958 0.1072485384
## 255 256 257 258 259
## -0.2209768567 -0.3017163231 -0.0375685420 0.0570896392 -0.1538909235
## 260 261 262 263 264
## -0.2009558465 0.0293518255 -0.0561042367 -0.2010049478 0.0864297269
## 265 266 267 268 269
## -0.1473870790 -0.0022179643 -0.3155888998 0.1359295400 -0.2700443246
## 270 271 272 273 274
## 0.3959021332 -0.0712077442 0.1883091508 -0.1654777886 -0.3081536581
## 275 276 277 278 279
## 0.0007089265 -0.0531822471 -0.4335907088 -0.0913175170 0.0613128537
## 280 281 282 283 284
## -0.2642509784 -0.0263912153 0.0086749298 -0.1681298841 0.0788645541
## 285 286 287 288 289
## -0.1524532506 0.2020784779 0.0937343444 -0.1162750269 -0.1416532676
## 290 291 292 293 294
## -0.2982481644 -0.1496078734 -1.2524779736 -0.3048938154 0.6609610801
## 295 296 297 298 299
## 0.5397187457 -0.0075262312 0.1320070578 0.3108173288 -0.2799082907
## 300 301 302 303 304
## 0.1512174843 0.2406220204 -0.1673251286 0.0773874138 -0.0287314645
## 305 306 307 308 309
## -0.4632487709 0.1786821601 -0.0416407075 0.2186550104 0.0727769785
## 310 311 312 313 314
## 0.1407108662 -0.2248459064 0.0323964131 -0.0888312646 0.0647049304
## 315 316 317 318 319
## 0.1130158270 0.3954531491 -0.1127523731 0.2839504974 -0.0250946533
## 320 321 322 323 324
## 0.0699236576 -0.0873765811 0.1822732678 -0.0524892235 -0.1313221403
## 325 326 327 328 329
## 0.1896033194 -0.0379981822 -0.4585078784 0.3170923344 0.8274083898
## 330 331 332 333 334
## 0.0170256029 0.3331875864 -0.0956242470 0.2653746905 -0.0868932508
## 335 336 337 338 339
## 0.4428391809 -0.1879427310 -0.1522270214 0.0088633796 -0.0994680309
## 340 341 342 343 344
## -0.0640388311 -0.1319802778 0.0309371281 0.0970880798 0.0526235860
## 345 346 347 348 349
## 0.3642435987 -0.0122921656 0.2983885408 0.2174855792 0.3614189279
## 350 351 352 353 354
## 0.2396446189 0.3824789125 0.2370636112 0.4664127077 0.3852501660
## 355 356 357 358 359
## 0.3912315500 -0.0534632855 -0.7024882832 0.7315535826 0.5664827855
## 360 361 362 363 364
## 0.5103028299 0.4049679414 0.4882264174 -0.1039341230 -0.2937518809
## 365 366 367 368 369
## 0.3664235209 0.3806250199 0.2264494251 0.2979040749 0.0046701908
## 370 371 372 373 374
## -0.0388709765 -0.3638722967 -0.2258985448 0.2799558245 -0.0833916842
## 375 376 377 378 379
## 0.1006425781 -0.0324932439 -0.0414415950 -0.2283320322 -1.6211632191
## 380 381 382 383 384
## 0.2155942026 0.5984436769 0.5513846964 0.3097721694 0.0141105734
## 385 386 387 388 389
## -0.3504824320 -0.0155012726 0.0550026094 -0.1060995104 -0.0362676052
## 390 391 392 393 394
## -0.0669212244 -0.1038404990 -0.2445221009 -0.0321315667 0.1935611142
## 395 396 397 398 399
## -0.1990305844 0.1288498802 -0.1395165988 0.0810524377 -0.2233803843
## 400 401 402 403 404
## -0.1412669936 0.2346628462 -0.0557033871 0.0035785463 0.0205284953
## 405 406 407 408 409
## 0.0575236295 -0.1259511953 -0.6486448488 0.1294277638 -0.3260230531
## 410 411 412 413 414
## -0.2641930418 -0.1117633802 0.0399188771 -0.0017608465 -0.0033773442
## 415 416 417 418 419
## -0.1698381287 -0.0690817436 -0.3251908652 -0.1149418965 0.4609519715
## 420 421 422 423 424
## -0.5726712724 -1.0233111481 0.1999347262 -0.4071212924 -0.3016727155
## 425 426 427 428 429
## 0.0929600487 -0.3234051885 -0.5504271923 0.5602989348 -0.4994594928
## 430 431 432 433 434
## -0.1733323786 -0.2852291210 -0.6526409194 0.3512642487 0.1878077627
## 435 436 437 438 439
## -0.1274407388 -0.3664902188 0.0707644576 0.9624969937 -0.2920790764
## 440 441 442 443 444
## 0.0287956529 -0.2419904170 0.2549506243 0.1771499983 -0.1969683895
## 445 446 447 448 449
## 0.1487716383 0.2628499292 -0.1876762151 -0.3991412032 0.4333106292
## 450 451 452 453 454
## -0.6711290534 1.0230188793 0.0956138993 0.1545294982 -0.3716568823
## 455 456 457 458 459
## 0.0648148703 0.0006020451 0.1708435560 0.0955116158 0.2311994734
## 460 461 462 463 464
## 0.2781582430 -0.1864942575 -0.4888360821 0.4620323943 0.4795995133
## 465 466 467 468 469
## 0.2138113196 0.2799563701 0.3758826737 -0.3528637019 0.0608659002
## 470 471 472 473 474
## -0.7088603430 0.5129318160 0.0411735522 0.0752466074 0.1795057709
## 475 476 477 478 479
## -0.2067345078 -0.3160843719 -0.0290998807 0.4062518168 -0.0794030696
## 480 481 482 483 484
## 0.3694185445 -0.0056020483 0.0583290481 0.0679268293 0.0317987549
## 485 486 487 488 489
## 0.1776004512 0.0178536066 0.1775098096 0.0390829284 0.0003528169
## 490
## 0.1904342536
remove <- list(p =list(TAVG=c(1:11),mean_precipation=c(1:11)))
mod_ardl1311_weather_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_meck_train,
p=11,q=13,
remove = remove)
f_ardl1311_weather_meck <- forecast(mod_ardl1311_weather_meck, x= t(full_cases_wastewater_weather_data_meck_test[,c(8,5,6)]),h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl1311_weather_meck$forecasts)
## [1] 0.2487683
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl1311_weather_meck$forecasts)
## [1] 0.2215939
checkresiduals(mod_ardl1311_weather_meck)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## 0.0158737146 0.1191886122 0.0574314550 -0.1094952895 -0.1645733032
## 19 20 21 22 23
## -0.0672699904 0.2563075688 0.0363321861 -0.0009455866 -0.0389911733
## 24 25 26 27 28
## 0.2758936892 0.0952516351 -0.1883819807 -0.0333570577 0.2158247308
## 29 30 31 32 33
## -0.0100698372 -0.0232497585 0.0296169483 -0.1359132937 -0.0323663445
## 34 35 36 37 38
## -0.3107204910 0.4466207935 0.0548089602 -0.0465662334 -0.0483215325
## 39 40 41 42 43
## -0.1613841887 0.1639665518 0.1871567400 -0.0048842122 -0.1101190278
## 44 45 46 47 48
## 0.1458180436 -0.0553780080 -0.1688691061 0.1855564280 -0.2617507911
## 49 50 51 52 53
## 0.3338265209 -0.1990200605 -0.2922552262 0.1767991827 -0.0163890012
## 54 55 56 57 58
## 0.0439883480 0.0310437118 -0.1292291167 0.3547549395 -0.3257337222
## 59 60 61 62 63
## 0.1761836270 -0.9948175753 -0.3343415233 0.1472259342 -0.5357874370
## 64 65 66 67 68
## 0.5309236620 0.3761237716 0.0829560907 0.1656709891 0.2486686713
## 69 70 71 72 73
## 0.3510848996 0.2367437083 -0.0927649268 0.0078838295 -0.1338419375
## 74 75 76 77 78
## 0.2099364952 0.0521075692 0.3847165935 0.3920960163 0.2809831519
## 79 80 81 82 83
## -0.0126571048 -0.0169812612 -0.1719966020 -0.2676293799 -0.1789864947
## 84 85 86 87 88
## -0.1040711941 0.2690701781 -0.2729825539 0.4056434410 0.0769264328
## 89 90 91 92 93
## 0.2738039807 -0.1952520178 -0.0562393218 -0.0708750471 -0.4677945571
## 94 95 96 97 98
## -0.0932064711 -0.2012010955 0.1178310695 0.0165016620 0.0686019854
## 99 100 101 102 103
## -0.0118492009 -0.0093642692 0.1912197679 -0.0094658407 -0.3916785598
## 104 105 106 107 108
## 0.3007933977 -0.5220230463 0.5658464688 -0.0634008294 -0.1226736376
## 109 110 111 112 113
## 0.1246573888 -0.3395573899 0.1097060155 0.3243776394 -0.1744775351
## 114 115 116 117 118
## -0.0515667868 -0.1764144834 -0.4177612298 0.3796194006 -0.3818854875
## 119 120 121 122 123
## -0.0228050064 -0.2062900875 0.0812646453 -0.1101771454 0.0946238868
## 124 125 126 127 128
## -0.3563966159 0.0591460039 0.2551893999 -0.2567295322 -0.6183574270
## 129 130 131 132 133
## -0.3455809985 -0.7845314846 -0.0900439215 -0.1384478021 0.6821814842
## 134 135 136 137 138
## 0.1204405705 0.1726842640 -0.0542289729 -0.1288603035 0.2426178544
## 139 140 141 142 143
## -0.4984207458 -0.2193024030 0.1893662071 -0.3320134899 -0.6201061756
## 144 145 146 147 148
## 0.5455639461 0.4139741381 0.0800026652 -0.0026186138 -0.1336317498
## 149 150 151 152 153
## -0.3408138696 0.8389974225 0.0435887991 -0.6998545630 -0.4130747487
## 154 155 156 157 158
## 0.3009301190 -0.1030574348 -0.2422273098 -0.0816572756 0.2522217610
## 159 160 161 162 163
## 0.1417016658 -0.3585542275 0.4501881686 0.3542186698 0.2498923126
## 164 165 166 167 168
## 0.2004700631 -0.3199266089 -0.3544502962 -0.2904129132 0.3721171546
## 169 170 171 172 173
## -0.6516905737 -0.6914395828 -0.6246059968 0.3860183227 -0.1300577859
## 174 175 176 177 178
## -0.6210884036 0.2829620951 0.2381189825 -0.1788815880 0.1251047846
## 179 180 181 182 183
## -0.1771922377 0.8311654548 0.2573304351 0.1454530017 -0.3849041120
## 184 185 186 187 188
## 0.0182911252 -0.3866730643 0.1027032108 0.3080459288 0.4038257782
## 189 190 191 192 193
## 0.4211338248 0.2487343775 -0.1416875521 0.2101165099 -0.2318115563
## 194 195 196 197 198
## -0.1499914417 -0.1007594881 -0.2155730486 0.7223806072 -0.1243255148
## 199 200 201 202 203
## 0.2132001993 0.1330607866 0.1359933895 0.2219120062 0.1331209204
## 204 205 206 207 208
## 0.1334922027 -0.0614375276 -0.2055712660 0.0575336152 0.0544301044
## 209 210 211 212 213
## -0.1399901670 0.0960978861 0.1220858351 -0.0315250406 -0.1636483722
## 214 215 216 217 218
## -0.0797690500 0.1424769260 -0.0807805676 -0.2108874504 0.1136784514
## 219 220 221 222 223
## -0.0991636657 0.0005695359 0.1490375414 0.0641720539 0.0516117587
## 224 225 226 227 228
## -0.2557262184 0.0158092476 -0.0325518999 0.1357941130 0.0042893021
## 229 230 231 232 233
## 0.1634441170 0.1139710669 0.0789295175 0.1597189708 0.1673319984
## 234 235 236 237 238
## -0.1942231608 -0.1803889536 -0.1132511347 0.1042327732 -0.1276703621
## 239 240 241 242 243
## -0.0979503539 0.1178464226 -0.0932191341 -0.2045959156 0.0854291315
## 244 245 246 247 248
## -0.0070849990 -0.1163745736 0.0225616467 -0.8433853874 0.5396427749
## 249 250 251 252 253
## 0.1804158145 0.2798251809 0.1172630687 0.1340594909 -0.1530311930
## 254 255 256 257 258
## 0.1422036958 -0.1632186165 -0.3425982138 -0.1821317893 -0.0492521459
## 259 260 261 262 263
## -0.1508064317 -0.2036391792 0.0593469658 -0.0501316698 -0.1931030232
## 264 265 266 267 268
## 0.1290562021 -0.1163581066 -0.0198323521 -0.3181038788 0.1649761890
## 269 270 271 272 273
## -0.2394216331 0.4049603545 -0.0308865762 0.1987983846 -0.1464230101
## 274 275 276 277 278
## -0.2488212421 0.0436514055 -0.0676581371 -0.4400354084 -0.1134816001
## 279 280 281 282 283
## 0.0206295985 -0.2824440598 0.0110098602 0.0457117095 -0.1181096940
## 284 285 286 287 288
## 0.0821548624 -0.1294966210 0.2343558286 0.0780350225 -0.0975202390
## 289 290 291 292 293
## -0.1163938941 -0.3473691643 -0.1669149157 -1.1985656861 -0.3466319734
## 294 295 296 297 298
## 0.6291373098 0.5916967934 0.1083403147 0.3027695994 0.4596312306
## 299 300 301 302 303
## -0.1755506319 0.2235341747 0.2145392956 -0.3513029711 -0.1716800675
## 304 305 306 307 308
## -0.1044548103 -0.4579931085 0.1506511341 -0.0636453704 0.1981570648
## 309 310 311 312 313
## 0.0295527237 0.1194162166 -0.2157289679 0.0242104586 -0.0383068807
## 314 315 316 317 318
## 0.1135450482 0.0458665230 0.2688698147 -0.1325394696 0.2173243088
## 319 320 321 322 323
## -0.0105760882 0.0962588459 -0.1452890034 0.0895038732 -0.1068657352
## 324 325 326 327 328
## -0.2095346309 0.1629866463 -0.0609950801 -0.4991670667 0.2410300166
## 329 330 331 332 333
## 0.8105635466 0.0531705353 0.3747566143 -0.0282769714 0.3151841861
## 334 335 336 337 338
## -0.0545672954 0.4762975470 -0.1873769151 -0.2565359099 -0.0630189946
## 339 340 341 342 343
## -0.0827415812 -0.0385979326 -0.1277227849 0.0852038521 0.0506385085
## 344 345 346 347 348
## -0.0128577471 0.3944445607 0.0472551578 0.2805069026 0.1921452034
## 349 350 351 352 353
## 0.3830751235 0.2043808145 0.3132038192 0.1898493332 0.3688528703
## 354 355 356 357 358
## 0.3070221289 0.3561671038 -0.1162356295 -0.8077344548 0.6183725338
## 359 360 361 362 363
## 0.4839856828 0.5023002081 0.3650093659 0.4086356492 -0.1349365882
## 364 365 366 367 368
## -0.3058305809 0.3591279580 0.2987514275 0.0657781302 0.2052432923
## 369 370 371 372 373
## 0.0870807256 0.0507408014 -0.2370787470 -0.1304178007 0.2981116418
## 374 375 376 377 378
## -0.1591948174 0.0348666159 0.0018689451 0.1015877929 -0.1683735809
## 379 380 381 382 383
## -1.6681054055 0.2444465826 0.4945394142 0.4686368846 0.4236487965
## 384 385 386 387 388
## 0.0866157284 -0.2472811680 0.1519131274 0.2506312144 -0.0530560030
## 389 390 391 392 393
## -0.2240944661 -0.2658850637 -0.1194835269 -0.2118159491 0.0619235780
## 394 395 396 397 398
## 0.2358100783 -0.2578144670 0.0963706791 -0.0779806537 0.1016122469
## 399 400 401 402 403
## -0.2044577917 -0.1074287878 0.2132434815 -0.1168794108 -0.0091786027
## 404 405 406 407 408
## 0.0545625358 0.0425910357 -0.0958359137 -0.5192578616 0.1672377594
## 409 410 411 412 413
## -0.3018072864 -0.2363497605 -0.0416518207 0.0427226727 0.0624456278
## 414 415 416 417 418
## 0.1846123641 -0.0280293762 0.0601456006 -0.2910083783 -0.1418309132
## 419 420 421 422 423
## 0.4589889351 -0.5769359760 -0.9588011142 0.2068689738 -0.3477767305
## 424 425 426 427 428
## -0.2012181232 0.1988488575 -0.2922556261 -0.4820601576 0.7467401459
## 429 430 431 432 433
## -0.2651484874 0.0268347445 -0.2684883340 -0.6899292206 0.3422417228
## 434 435 436 437 438
## 0.1582684440 -0.0375826477 -0.3841446834 -0.0181625459 0.9886537225
## 439 440 441 442 443
## -0.1638454244 0.0950672555 -0.2371768380 0.1403236707 0.1225477020
## 444 445 446 447 448
## -0.1760909432 0.1190934209 0.1336165703 -0.3424671647 -0.4271470724
## 449 450 451 452 453
## 0.4677305362 -0.7400281423 1.0217398401 0.0783359554 0.0816893328
## 454 455 456 457 458
## -0.4090480932 0.0042204539 0.0140112817 0.0854735645 -0.0323518619
## 459 460 461 462 463
## 0.1022436393 0.1984354308 -0.1993437734 -0.4165408393 0.3997853001
## 464 465 466 467 468
## 0.4143609060 0.1289833992 0.2344193175 0.4038177123 -0.3690978430
## 469 470 471 472 473
## 0.0212369229 -0.6549080304 0.4145359880 -0.1230323563 -0.0634018220
## 474 475 476 477 478
## 0.1551319643 -0.2349890515 -0.3120571059 -0.0006542899 0.4892901762
## 479 480 481 482 483
## -0.1339658176 0.1679545588 -0.1141280845 0.0117768968 0.0305786997
## 484 485 486 487 488
## 0.0545905569 0.1469298736 -0.1144001991 0.0931871094 0.0550377171
## 489 490
## 0.0064183479 0.1455704804
remove <- list(p =list(TAVG=c(1:14),mean_precipation=c(1:14)))
mod_ardl914_weather_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_meck_train,
p=14,q=9,
remove = remove)
remove <- list(p =list(TAVG=c(1:14),mean_precipation=c(1:14)))
mod_ardl914_weather_meck <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
TAVG,data = full_cases_wastewater_weather_data_meck_train,
p=14,q=9,
remove = remove)
summary(mod_ardl914_weather_meck)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.60579 -0.16172 0.00929 0.17423 1.01182
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.340915 0.488841 -0.697 0.485916
## log_viral_gene.t -0.062055 0.035360 -1.755 0.079954 .
## log_viral_gene.1 0.119283 0.046192 2.582 0.010129 *
## log_viral_gene.2 -0.048323 0.046095 -1.048 0.295051
## log_viral_gene.3 0.115203 0.046173 2.495 0.012953 *
## log_viral_gene.4 -0.109250 0.046488 -2.350 0.019202 *
## log_viral_gene.5 0.068536 0.046770 1.465 0.143513
## log_viral_gene.6 -0.071897 0.047002 -1.530 0.126800
## log_viral_gene.7 0.048087 0.046624 1.031 0.302918
## log_viral_gene.8 -0.013162 0.046546 -0.283 0.777472
## log_viral_gene.9 -0.007683 0.046473 -0.165 0.868757
## log_viral_gene.10 0.015626 0.045933 0.340 0.733877
## log_viral_gene.11 0.034814 0.045823 0.760 0.447800
## log_viral_gene.12 -0.048558 0.045715 -1.062 0.288720
## log_viral_gene.13 -0.072942 0.045146 -1.616 0.106861
## log_viral_gene.14 0.049557 0.034603 1.432 0.152792
## mean_precipation.t -0.086905 0.059140 -1.469 0.142404
## TAVG.t 0.001617 0.001151 1.406 0.160507
## log_mean_new_cases.1 0.515709 0.047062 10.958 < 2e-16 ***
## log_mean_new_cases.2 0.050023 0.052925 0.945 0.345083
## log_mean_new_cases.3 0.207197 0.052849 3.921 0.000102 ***
## log_mean_new_cases.4 0.055063 0.053651 1.026 0.305300
## log_mean_new_cases.5 0.136893 0.053930 2.538 0.011476 *
## log_mean_new_cases.6 0.076001 0.053685 1.416 0.157556
## log_mean_new_cases.7 0.002560 0.052938 0.048 0.961449
## log_mean_new_cases.8 0.011205 0.053208 0.211 0.833299
## log_mean_new_cases.9 -0.089535 0.047957 -1.867 0.062554 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3118 on 449 degrees of freedom
## Multiple R-squared: 0.9248, Adjusted R-squared: 0.9205
## F-statistic: 212.4 on 26 and 449 DF, p-value: < 2.2e-16
f_ardl914_weather_meck <- forecast(mod_ardl914_weather_meck,
x= t(full_cases_wastewater_weather_data_meck_test[,c(8,5,6)]),
h=14,
interval = TRUE)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl914_weather_meck$forecasts[,2])
## [1] 0.1278721
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_ardl914_weather_meck$forecasts[,2])
## [1] 0.1061923
checkresiduals(mod_ardl914_weather_meck)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## 0.0201283190 0.0488150294 -0.1212445118 -0.1326995689 -0.0260273329
## 20 21 22 23 24
## 0.2363100520 -0.0069240528 0.0325582815 -0.0439697482 0.2647168202
## 25 26 27 28 29
## 0.0822631479 -0.2285264329 -0.0432912887 0.2847376330 0.0670551627
## 30 31 32 33 34
## -0.0408452932 0.0110197700 -0.1463728842 -0.0486978196 -0.3357647354
## 35 36 37 38 39
## 0.4415179971 0.0391517393 -0.0725094928 -0.1077128360 -0.2280820437
## 40 41 42 43 44
## 0.1799130977 0.1427038608 -0.1175441095 -0.1253020780 0.2619775775
## 45 46 47 48 49
## -0.0296655180 -0.1984936111 0.1660925722 -0.2657746868 0.4203046113
## 50 51 52 53 54
## -0.1704374764 -0.3356754813 0.1579798005 -0.0221529676 0.0243912911
## 55 56 57 58 59
## 0.0264425661 -0.1051552698 0.3299146517 -0.3036299290 0.1765093991
## 60 61 62 63 64
## -1.0413487663 -0.3008866089 0.2000447140 -0.4356764335 0.6144193380
## 65 66 67 68 69
## 0.3455960693 0.1339947187 0.1338025037 0.2564116715 0.2944261365
## 70 71 72 73 74
## 0.1859188551 0.0044690629 0.0291801799 -0.0757405338 0.2407017225
## 75 76 77 78 79
## 0.0621641989 0.3590910071 0.2465377375 0.1916996835 -0.1167738608
## 80 81 82 83 84
## -0.1170935287 -0.2590382822 -0.4345162313 -0.1564978651 0.1124205770
## 85 86 87 88 89
## 0.3529894322 -0.2180826280 0.3850756895 0.0235386862 0.2154448141
## 90 91 92 93 94
## -0.2333332317 -0.0758013935 -0.0092868825 -0.3902992019 -0.0149761140
## 95 96 97 98 99
## -0.1888239975 0.1272603703 0.0108878584 0.0605564862 -0.0498895291
## 100 101 102 103 104
## -0.0653001936 0.1725358448 -0.0720018916 -0.3440465910 0.3256178382
## 105 106 107 108 109
## -0.6132325043 0.5932079887 -0.0307810632 -0.1299989369 0.1330739435
## 110 111 112 113 114
## -0.2921760430 0.1217264632 0.2577252518 -0.1108776203 -0.0568978445
## 115 116 117 118 119
## -0.1500607459 -0.4220268469 0.2946226254 -0.4004986241 -0.0773630385
## 120 121 122 123 124
## -0.2053811059 0.1080115271 -0.1848536325 0.0194957682 -0.3977712711
## 125 126 127 128 129
## -0.0108496389 0.2079484992 -0.2651016708 -0.5713934918 -0.2665189185
## 130 131 132 133 134
## -0.6987143002 0.0220496472 -0.0819594102 0.6430981555 0.1291788495
## 135 136 137 138 139
## 0.1555141041 -0.2256247425 -0.3182154388 0.2458704973 -0.5753080221
## 140 141 142 143 144
## -0.2447128990 0.2864609232 -0.3102346320 -0.6472301657 0.4545869389
## 145 146 147 148 149
## 0.2888571398 0.0046638524 0.0677896022 -0.1436797761 -0.2975435328
## 150 151 152 153 154
## 0.9302083551 -0.0478129245 -0.6818959202 -0.3007382440 0.2227184605
## 155 156 157 158 159
## -0.1616353022 -0.1546323230 -0.1055656302 0.1200162040 0.1826333643
## 160 161 162 163 164
## -0.4303634296 0.2756662181 0.2110187825 0.3555622651 0.3142907940
## 165 166 167 168 169
## -0.4250075334 -0.3458685426 -0.2156838276 0.4979862007 -0.6254678315
## 170 171 172 173 174
## -0.5871599468 -0.4951690596 0.4226674172 -0.1374607712 -0.7125665982
## 175 176 177 178 179
## 0.2108929774 0.2564666159 -0.2388332648 -0.0424545135 -0.2487124340
## 180 181 182 183 184
## 0.9244455776 0.2521773160 0.0320575630 -0.3748313302 0.1091830472
## 185 186 187 188 189
## -0.2448141070 0.1253664267 0.3404142609 0.4132420921 0.5462058477
## 190 191 192 193 194
## 0.3309711639 -0.2234567977 0.1895366953 -0.1882241425 -0.1086226271
## 195 196 197 198 199
## -0.0002795538 -0.0568951368 0.8427797233 -0.1044659888 0.1457173324
## 200 201 202 203 204
## 0.0517476540 0.1855636861 0.2121105867 0.1422296510 0.1961586697
## 205 206 207 208 209
## -0.0197928331 -0.1472176952 0.0726175850 0.1154343015 -0.0689374469
## 210 211 212 213 214
## 0.1357691734 0.1499241883 -0.0314317300 -0.2329401572 -0.1256030631
## 215 216 217 218 219
## 0.1633746729 -0.0374837702 -0.1833350212 0.0903962117 -0.0711035508
## 220 221 222 223 224
## -0.0228528772 0.1344623395 0.0810455426 0.0289270733 -0.2191975792
## 225 226 227 228 229
## 0.0417125843 -0.0390216287 0.1895948591 0.0002243875 0.1349596695
## 230 231 232 233 234
## 0.1563756467 0.0641035810 0.0866483768 0.1034920253 -0.2541776775
## 235 236 237 238 239
## -0.1843944828 -0.0723875999 0.1450551646 -0.1128776869 -0.1157265536
## 240 241 242 243 244
## 0.0942295273 -0.0995244525 -0.2171402609 0.0047886619 -0.0868715720
## 245 246 247 248 249
## -0.1291132014 0.0437669475 -0.8928762829 0.5112494993 0.1518523876
## 250 251 252 253 254
## 0.2029801182 0.0259306496 0.1178250176 -0.1620502577 0.0958860781
## 255 256 257 258 259
## -0.1891556641 -0.3873468839 -0.0434896657 0.0614287367 -0.1435505630
## 260 261 262 263 264
## -0.1943626312 0.0464628027 -0.0676627395 -0.1836972247 0.0978056988
## 265 266 267 268 269
## -0.1619764374 -0.0066188676 -0.3003855493 0.1427711298 -0.2749812721
## 270 271 272 273 274
## 0.4054028500 -0.0585238430 0.1720090134 -0.1435544863 -0.3111503525
## 275 276 277 278 279
## 0.0151947242 -0.0784707326 -0.4203035576 -0.1209718526 0.0853501505
## 280 281 282 283 284
## -0.2630570451 -0.0097176033 0.0217739055 -0.1805067177 0.0894963125
## 285 286 287 288 289
## -0.1290611624 0.1878877812 0.0883200902 -0.0987111860 -0.1539851700
## 290 291 292 293 294
## -0.3058282129 -0.1394998610 -1.2657394464 -0.2964238430 0.6556146678
## 295 296 297 298 299
## 0.5640545389 0.0397205897 0.1567183869 0.3413238396 -0.2769593710
## 300 301 302 303 304
## 0.1839986251 0.1582594591 -0.2607158111 0.0688198927 0.0030143123
## 305 306 307 308 309
## -0.4678111034 0.1604046778 -0.0216893350 0.1851310486 0.0643104666
## 310 311 312 313 314
## 0.1669077490 -0.2360229824 0.0301671399 -0.0678648256 0.0184729591
## 315 316 317 318 319
## 0.1150075333 0.3836581991 -0.1093838493 0.2765331599 -0.0147658842
## 320 321 322 323 324
## 0.0424690048 -0.1035010061 0.1593947591 -0.0594280641 -0.1482651978
## 325 326 327 328 329
## 0.2054185576 -0.0611675068 -0.4521366763 0.3088948699 0.8317678125
## 330 331 332 333 334
## 0.0094925732 0.3444435840 -0.0803254738 0.2535385979 -0.0751852975
## 335 336 337 338 339
## 0.4518706579 -0.2383406292 -0.1917932280 0.0511779478 -0.1080730236
## 340 341 342 343 344
## -0.0486817126 -0.1496596507 0.0432020769 0.0758517456 0.0848001098
## 345 346 347 348 349
## 0.3707296165 -0.0330324572 0.3021538905 0.2079225313 0.3525140059
## 350 351 352 353 354
## 0.2311489351 0.3682833555 0.2249327910 0.4246291085 0.3790118669
## 355 356 357 358 359
## 0.3584425530 -0.0723131399 -0.7280857993 0.7183999157 0.5446988555
## 360 361 362 363 364
## 0.5054746228 0.3910730824 0.4835643544 -0.0978374034 -0.2828114955
## 365 366 367 368 369
## 0.3764994366 0.2677914730 0.2207114119 0.3164008377 0.0274361339
## 370 371 372 373 374
## -0.0072345778 -0.3303328434 -0.2148824675 0.2411740335 -0.1052125927
## 375 376 377 378 379
## 0.1180519765 -0.0208608354 -0.0135154079 -0.2076882045 -1.6057928545
## 380 381 382 383 384
## 0.2023905050 0.5626318024 0.5843278780 0.3296332474 0.0325247466
## 385 386 387 388 389
## -0.3158350731 0.0138877175 0.1206834505 -0.2325783333 -0.0899623800
## 390 391 392 393 394
## -0.0515088696 -0.0800730623 -0.2081954678 -0.0149166863 0.1628597724
## 395 396 397 398 399
## -0.2144053530 0.1487403432 -0.1266828330 0.0891185964 -0.2150317425
## 400 401 402 403 404
## -0.1405795408 0.2247485400 -0.0714916600 0.0310274271 0.0095112489
## 405 406 407 408 409
## 0.0721484129 -0.1139767239 -0.6319492888 0.1347349159 -0.3339801720
## 410 411 412 413 414
## -0.2350850446 -0.0925018697 0.0519996810 0.0262323211 0.0239706564
## 415 416 417 418 419
## -0.1210319847 -0.0902867793 -0.2969519786 -0.1089753036 0.4488886232
## 420 421 422 423 424
## -0.5614778179 -1.0145384308 0.2060284186 -0.3726424204 -0.2782998785
## 425 426 427 428 429
## 0.1281983169 -0.3079515360 -0.5520580365 0.6365216116 -0.4493224737
## 430 431 432 433 434
## -0.2112375409 -0.2488498463 -0.6439388068 0.3456390686 0.2083050044
## 435 436 437 438 439
## -0.1158269722 -0.4284632083 0.1220175448 0.9734936680 -0.2989246798
## 440 441 442 443 444
## 0.0438419779 -0.2955115509 0.2414808957 0.1959026982 -0.2008684833
## 445 446 447 448 449
## 0.1100371765 0.1986834017 -0.1385911511 -0.4222284458 0.4183589866
## 450 451 452 453 454
## -0.7059813316 1.0118186719 0.1168122849 0.1405620212 -0.3802367067
## 455 456 457 458 459
## 0.0667790796 -0.0077305667 0.0975681065 0.1293569262 0.1358811582
## 460 461 462 463 464
## 0.3141217011 -0.1658673783 -0.4843261887 0.4207965053 0.4549704123
## 465 466 467 468 469
## 0.1952991999 0.2796675198 0.3572061322 -0.3522744006 0.0790238488
## 470 471 472 473 474
## -0.7132441820 0.4320866851 0.0090954243 0.0841965604 0.1804996445
## 475 476 477 478 479
## -0.2165604539 -0.2766053560 -0.0626253799 0.4199812622 -0.1489028740
## 480 481 482 483 484
## 0.3668738278 -0.0042531929 0.0368610670 0.0795556153 0.0152495691
## 485 486 487 488 489
## 0.1352920769 -0.0227313652 0.2013421224 0.0243414321 0.0052767780
## 490
## 0.1734647060
exp(f_ardl914_weather_meck$forecasts[1,2])
## [1] 3.629081
exp(f_ardl914_weather_meck$forecasts[1,1])
## [1] 2.013232
exp(f_ardl914_weather_meck$forecasts[1,3])
## [1] 6.643546
exp(f_ardl914_weather_meck$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_meck_test[1,7])
## [1] 0.6029537
exp(f_ardl914_weather_meck$forecasts[7,2])
## [1] 3.720462
exp(f_ardl914_weather_meck$forecasts[7,1])
## [1] 1.614414
exp(f_ardl914_weather_meck$forecasts[7,3])
## [1] 9.171205
exp(f_ardl914_weather_meck$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_meck_test[7,7])
## [1] -0.1339966
exp(f_ardl914_weather_meck$forecasts[14,2])
## [1] 3.909254
exp(f_ardl914_weather_meck$forecasts[14,1])
## [1] 1.261592
exp(f_ardl914_weather_meck$forecasts[14,3])
## [1] 11.72392
exp(f_ardl914_weather_meck$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_meck_test[14,7])
## [1] 0.8893137
#New Hanover
full_cases_wastewater_weather_data_hanover <-
full_cases_wastewater_weather_data_hanover[-c(505,506,507),]
full_cases_wastewater_weather_data_hanover <- full_cases_wastewater_weather_data_hanover %>%
mutate(log_mean_new_cases = log(mean_new_cases),
log_viral_gene = log(full_viral_gene_copies_per_person))
full_cases_wastewater_weather_data_hanover <- full_cases_wastewater_weather_data_hanover %>%
mutate(log_mean_new_cases = seasadj(decompose(ts(log_mean_new_cases, frequency=7))),
log_viral_gene = seasadj(decompose(ts(log_viral_gene, frequency=7))))
full_cases_wastewater_weather_data_hanover_train <-
full_cases_wastewater_weather_data_hanover[-c(491:504),]
full_cases_wastewater_weather_data_hanover_test <-
full_cases_wastewater_weather_data_hanover[c(491:504),]
lowest_rmse_hanover <- Inf
best_mod_hanover <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train, p=p,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_hanover_test[,7]),h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_hanover){
lowest_rmse_hanover<- forecast_acc
best_mod_hanover <-mod
}
}
}
lowest_rmse_hanover #0.348 (0.317)
## [1] 0.3413698
summary(best_mod_hanover)
##
## Time series regression with "ts" data:
## Start = 10, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.48883 -0.21033 0.00741 0.23862 1.15177
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.683459 0.225717 -3.028 0.00260 **
## log_viral_gene.t 0.073524 0.029404 2.500 0.01274 *
## log_viral_gene.1 -0.023619 0.040463 -0.584 0.55969
## log_viral_gene.2 -0.001439 0.029774 -0.048 0.96148
## log_mean_new_cases.1 0.457334 0.045959 9.951 < 2e-16 ***
## log_mean_new_cases.2 0.123586 0.050710 2.437 0.01518 *
## log_mean_new_cases.3 0.046925 0.050427 0.931 0.35256
## log_mean_new_cases.4 0.150204 0.050320 2.985 0.00298 **
## log_mean_new_cases.5 0.070798 0.050737 1.395 0.16356
## log_mean_new_cases.6 0.074289 0.050361 1.475 0.14085
## log_mean_new_cases.7 0.155353 0.050377 3.084 0.00216 **
## log_mean_new_cases.8 -0.058520 0.050537 -1.158 0.24746
## log_mean_new_cases.9 -0.100652 0.045641 -2.205 0.02792 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3794 on 468 degrees of freedom
## Multiple R-squared: 0.9009, Adjusted R-squared: 0.8984
## F-statistic: 354.7 on 12 and 468 DF, p-value: < 2.2e-16
tsdisplay(residuals(best_mod_hanover))
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -0.2937247715 0.0725525051 0.2357132291 0.0428823729 0.2024050180
## 15 16 17 18 19
## 0.1383610625 -0.2676940703 -0.0134268985 -0.0117135696 0.0764144973
## 20 21 22 23 24
## 0.1981303419 0.2113455282 0.2379975457 0.0051074184 -0.0491099861
## 25 26 27 28 29
## -0.1261627848 -0.2905892448 0.6591943825 -0.2276926085 0.3194060555
## 30 31 32 33 34
## -0.4551185306 0.1445597583 -0.0568366994 -0.0627825150 0.2938045965
## 35 36 37 38 39
## 0.3709020208 0.2960118006 -0.0942220382 -0.1734517743 0.0226241743
## 40 41 42 43 44
## 0.0270041027 0.1869636936 -0.2392370427 -0.3142958568 0.2411378355
## 45 46 47 48 49
## -0.0771738354 -0.1404487333 -0.3677277543 0.0431663383 -0.4316978812
## 50 51 52 53 54
## 0.2531292334 -0.1388129807 -0.4180790801 0.3174781199 -0.1916208740
## 55 56 57 58 59
## 0.1987007527 0.3663651337 0.2555273155 0.0239482523 -0.0530943676
## 60 61 62 63 64
## 0.1176959277 0.0485663629 0.1937034479 0.0685978034 -0.1774245281
## 65 66 67 68 69
## -0.4345144209 0.6653127842 0.1917715091 0.1800176281 -0.2190088185
## 70 71 72 73 74
## 0.4411357528 0.0434507919 -0.0425528122 0.0906556734 -0.1789678336
## 75 76 77 78 79
## 0.1817007557 0.4857756943 0.2444219798 0.1366642375 0.1156306111
## 80 81 82 83 84
## 0.4289515301 0.3184282752 0.1221898253 -0.0488892873 -0.1376011723
## 85 86 87 88 89
## 0.2397033861 -0.0037757774 0.2027015932 -0.3899420104 -0.0166538988
## 90 91 92 93 94
## -0.2101998536 0.0999245294 -0.2764622533 0.1196021546 -0.1969040255
## 95 96 97 98 99
## 0.4246182427 0.0866703371 -0.2692966292 0.1022241170 0.1845049143
## 100 101 102 103 104
## 0.2844814622 0.0567238754 0.0718908996 -0.0193711583 0.3085424980
## 105 106 107 108 109
## -0.2717931726 -1.1953301375 0.6730721267 -0.1633869109 0.3155728050
## 110 111 112 113 114
## -0.0091031336 0.3984023024 0.5548959808 -1.0566851701 0.7880259146
## 115 116 117 118 119
## 0.0939056670 0.1223389249 0.0491446447 0.1406920939 -0.6743811810
## 120 121 122 123 124
## 0.3197780047 0.2157982532 -0.5256451527 0.0489862102 -1.0499510287
## 125 126 127 128 129
## 0.4394807412 0.3652649330 -0.5195959156 0.3998504377 -0.1191334670
## 130 131 132 133 134
## 0.4433747581 -0.0947424623 0.0832120425 -0.5277903645 -0.1063871747
## 135 136 137 138 139
## 0.2841217598 -0.8616391162 -0.3790968311 0.7288172894 0.5071672677
## 140 141 142 143 144
## -0.2286002821 0.0314926421 -0.6829332184 0.9703729179 -0.7449079747
## 145 146 147 148 149
## 0.2679769867 -0.3756868031 0.2328898204 0.2944174911 -0.4603615280
## 150 151 152 153 154
## -0.2255009541 -0.0717132127 -0.1898146588 0.0234792637 0.3163682613
## 155 156 157 158 159
## 0.2111669824 -0.2559877586 -0.0066921052 -0.1121490904 -0.0041986795
## 160 161 162 163 164
## 0.0424280537 0.3866164312 0.3249911181 -0.4301015712 -0.0217016916
## 165 166 167 168 169
## -0.2131773712 0.0505797912 0.0663116210 0.2714930485 0.2043053345
## 170 171 172 173 174
## -0.3305856683 0.0199390521 -0.0987236863 -0.0879896828 -0.1770255319
## 175 176 177 178 179
## 0.9075754923 -0.1057388530 -0.4752423733 -0.1321610850 -0.3801484525
## 180 181 182 183 184
## 0.5419094734 -0.2656456412 0.1227014611 0.2842934188 -0.3350889685
## 185 186 187 188 189
## 0.5033548382 -0.0068548374 -0.6091154625 -0.2503721300 0.0775616818
## 190 191 192 193 194
## 0.8245964949 -0.3712032240 -0.6583240983 1.1415074891 0.0754030017
## 195 196 197 198 199
## 0.6061736284 -0.2877254417 -0.7529277730 -0.8836332442 0.7384886742
## 200 201 202 203 204
## 0.0897824100 0.7422410308 0.3995787787 0.7494566948 0.8276606603
## 205 206 207 208 209
## 0.1200761219 -0.0654303538 -0.2230863545 0.0274122666 -0.0400149964
## 210 211 212 213 214
## 0.0022512118 0.2936783139 0.0990719213 0.0543947860 -0.0493149906
## 215 216 217 218 219
## -0.0373004111 0.3833824395 0.0185383025 0.0589516846 0.0781896085
## 220 221 222 223 224
## 0.1379129373 -0.0118587807 -0.1957035215 0.1029201034 -0.1096721278
## 225 226 227 228 229
## 0.2728494624 0.2057127592 -0.1336138055 0.0636875549 0.2787792813
## 230 231 232 233 234
## -0.0819055576 -0.2028231242 0.1279166587 0.6104019865 0.5059773785
## 235 236 237 238 239
## 0.2927907643 0.3309247297 -0.2103299644 -0.6020374951 -0.2870039810
## 240 241 242 243 244
## -0.1242200552 0.1387655073 0.1208341292 0.1154879578 -0.1883789764
## 245 246 247 248 249
## -0.1700820686 -0.4658964526 -0.8623299961 0.6775253499 0.0105449122
## 250 251 252 253 254
## -0.0087829510 0.1708893966 -0.2762265336 -0.0240055186 0.3459538609
## 255 256 257 258 259
## -0.1418843551 -0.1564006393 -0.1053706580 0.1066407105 -0.1853499335
## 260 261 262 263 264
## -0.2487433641 -0.2333642650 -0.2727303989 -0.1687733447 -0.0466078025
## 265 266 267 268 269
## -0.3995324342 -0.0677488924 -0.0471187115 -0.0601087398 -0.1041610652
## 270 271 272 273 274
## -0.2367197351 -0.3989378404 0.2484457684 -0.1568777389 -0.7453024532
## 275 276 277 278 279
## 0.3555214858 0.1002671666 -0.3868654278 0.3040895309 -0.2028461658
## 280 281 282 283 284
## 0.1722189512 -0.2332142707 -0.0440658053 -0.3086458206 -0.0504900649
## 285 286 287 288 289
## 0.1012008512 0.1700433893 -0.3481999153 -0.3257685419 0.0074100728
## 290 291 292 293 294
## 0.0341751172 -1.4888343080 -0.7335710249 -0.5480315814 0.7716219916
## 295 296 297 298 299
## -0.3682446885 -0.0486605721 -0.1022491050 0.4153375971 -0.6283894824
## 300 301 302 303 304
## 0.2012134868 -0.5205160486 -0.1192180476 -0.0939335491 0.4307161292
## 305 306 307 308 309
## -0.1346345308 -0.6418514036 -0.1222579844 0.1329938855 0.1042333559
## 310 311 312 313 314
## 0.5206664141 -0.6846115233 -0.3201812611 0.0842644910 0.6126850050
## 315 316 317 318 319
## 0.5875763431 -0.4078496593 0.2353657459 0.3752687472 0.3007912347
## 320 321 322 323 324
## 0.0219233387 -0.5585097529 0.0920338782 0.4985910974 -0.2534512110
## 325 326 327 328 329
## -0.1352546575 -0.0338617618 -1.2401356127 -0.0603990799 0.6927204590
## 330 331 332 333 334
## 0.8101645216 0.4554625066 0.2758977507 -0.1558902425 0.2324918101
## 335 336 337 338 339
## -0.1571132546 -0.3554635846 0.1720243647 -0.0368614666 -0.2860883750
## 340 341 342 343 344
## 0.3664146703 0.3245726439 -0.8113220120 0.3094211668 0.1261280314
## 345 346 347 348 349
## 0.1013780624 0.5355813115 -0.2189059879 0.4203520863 0.4150589674
## 350 351 352 353 354
## 0.3031770151 0.1136186294 0.3525790847 0.0603945804 0.6853335007
## 355 356 357 358 359
## 0.3605603211 -0.5404365110 -0.6752436627 0.5970516429 0.8297212770
## 360 361 362 363 364
## 0.7278450588 0.5652834562 0.5630755331 -0.1175717912 -0.1903461945
## 365 366 367 368 369
## 0.0972404074 0.3422963065 0.3265283580 0.0821512567 0.4221394520
## 370 371 372 373 374
## 0.3144995798 0.0242426290 -0.0869549654 0.1292901847 0.0371106374
## 375 376 377 378 379
## 0.1510399797 0.1887376894 0.2498141128 -0.1476159290 -0.2584843004
## 380 381 382 383 384
## 0.2742931587 0.3827214873 0.2861100347 0.0320705553 -0.8687612922
## 385 386 387 388 389
## -0.6717371112 0.0901594979 0.3829023442 -0.0934348061 -0.0938720504
## 390 391 392 393 394
## 0.1243421596 0.0823670432 -0.4012690476 -0.3010281636 -0.0453070090
## 395 396 397 398 399
## -0.1682664417 -0.0227266962 -0.1872004916 -0.1452224339 -0.5144250145
## 400 401 402 403 404
## -0.1922387100 -0.0878008475 -0.0624489138 -0.2762842108 0.0024621932
## 405 406 407 408 409
## -0.0521510737 -0.7394339480 0.0295910486 -0.2974149703 -0.4524329524
## 410 411 412 413 414
## -0.0942575808 -0.2679268279 -0.1104944518 -0.5897524445 0.3438203257
## 415 416 417 418 419
## -0.1288860696 -0.2150139160 -0.0303903430 0.0037787687 -0.4397751792
## 420 421 422 423 424
## -0.6832706400 -0.4453951363 -0.1344499452 -0.8179229615 -0.4643839583
## 425 426 427 428 429
## 0.5094620775 -0.3647641012 0.3028159342 0.2062176388 0.1865326352
## 430 431 432 433 434
## -0.5719646627 0.1892242928 0.0735899417 -0.4111611070 0.2540204491
## 435 436 437 438 439
## 0.0494242221 -0.5904800236 -0.1388350201 -0.1684062474 -0.1357092483
## 440 441 442 443 444
## 0.1638572878 0.4641277285 0.9046284552 -0.5630378051 -0.2394969869
## 445 446 447 448 449
## -0.1976548938 -0.2692456496 0.0486816515 0.2693518653 0.1750217782
## 450 451 452 453 454
## -0.3212230719 -0.1564946816 -0.2735179742 -0.1829370659 -0.0562354176
## 455 456 457 458 459
## 0.2751055137 0.1558797044 0.1341932450 -0.3953978283 0.2066401363
## 460 461 462 463 464
## 0.6027321415 -0.6998549402 0.0009059039 -0.0013204327 0.0471160495
## 465 466 467 468 469
## 0.3756997387 0.7391826271 -0.3535968665 -0.1872812377 -0.4631693409
## 470 471 472 473 474
## -0.4225914438 0.2121285303 0.0406720251 -0.3903567773 -0.2813712050
## 475 476 477 478 479
## -0.5980437445 1.1517746897 -0.7341497203 0.2773720907 0.3208178831
## 480 481 482 483 484
## 0.3306062548 0.3199183622 0.5542635356 -0.8634054777 -0.1105232295
## 485 486 487 488 489
## 0.2386241573 -0.0339323640 0.1725353984 -0.1361991729 0.3281013347
## 490
## -0.0849704518
mod_ardl92_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
p=2,q=9)
summary(mod_ardl92_hanover)
##
## Time series regression with "ts" data:
## Start = 10, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.48883 -0.21033 0.00741 0.23862 1.15177
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.683459 0.225717 -3.028 0.00260 **
## log_viral_gene.t 0.073524 0.029404 2.500 0.01274 *
## log_viral_gene.1 -0.023619 0.040463 -0.584 0.55969
## log_viral_gene.2 -0.001439 0.029774 -0.048 0.96148
## log_mean_new_cases.1 0.457334 0.045959 9.951 < 2e-16 ***
## log_mean_new_cases.2 0.123586 0.050710 2.437 0.01518 *
## log_mean_new_cases.3 0.046925 0.050427 0.931 0.35256
## log_mean_new_cases.4 0.150204 0.050320 2.985 0.00298 **
## log_mean_new_cases.5 0.070798 0.050737 1.395 0.16356
## log_mean_new_cases.6 0.074289 0.050361 1.475 0.14085
## log_mean_new_cases.7 0.155353 0.050377 3.084 0.00216 **
## log_mean_new_cases.8 -0.058520 0.050537 -1.158 0.24746
## log_mean_new_cases.9 -0.100652 0.045641 -2.205 0.02792 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3794 on 468 degrees of freedom
## Multiple R-squared: 0.9009, Adjusted R-squared: 0.8984
## F-statistic: 354.7 on 12 and 468 DF, p-value: < 2.2e-16
f_ardl92_hanover <- forecast(mod_ardl92_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,7]),
h=14,
interval = TRUE)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl92_hanover$forecasts[,2])
## [1] 0.3413698
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl92_hanover$forecasts[,2])
## [1] 0.2535276
checkresiduals(mod_ardl92_hanover)
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -0.2937247715 0.0725525051 0.2357132291 0.0428823729 0.2024050180
## 15 16 17 18 19
## 0.1383610625 -0.2676940703 -0.0134268985 -0.0117135696 0.0764144973
## 20 21 22 23 24
## 0.1981303419 0.2113455282 0.2379975457 0.0051074184 -0.0491099861
## 25 26 27 28 29
## -0.1261627848 -0.2905892448 0.6591943825 -0.2276926085 0.3194060555
## 30 31 32 33 34
## -0.4551185306 0.1445597583 -0.0568366994 -0.0627825150 0.2938045965
## 35 36 37 38 39
## 0.3709020208 0.2960118006 -0.0942220382 -0.1734517743 0.0226241743
## 40 41 42 43 44
## 0.0270041027 0.1869636936 -0.2392370427 -0.3142958568 0.2411378355
## 45 46 47 48 49
## -0.0771738354 -0.1404487333 -0.3677277543 0.0431663383 -0.4316978812
## 50 51 52 53 54
## 0.2531292334 -0.1388129807 -0.4180790801 0.3174781199 -0.1916208740
## 55 56 57 58 59
## 0.1987007527 0.3663651337 0.2555273155 0.0239482523 -0.0530943676
## 60 61 62 63 64
## 0.1176959277 0.0485663629 0.1937034479 0.0685978034 -0.1774245281
## 65 66 67 68 69
## -0.4345144209 0.6653127842 0.1917715091 0.1800176281 -0.2190088185
## 70 71 72 73 74
## 0.4411357528 0.0434507919 -0.0425528122 0.0906556734 -0.1789678336
## 75 76 77 78 79
## 0.1817007557 0.4857756943 0.2444219798 0.1366642375 0.1156306111
## 80 81 82 83 84
## 0.4289515301 0.3184282752 0.1221898253 -0.0488892873 -0.1376011723
## 85 86 87 88 89
## 0.2397033861 -0.0037757774 0.2027015932 -0.3899420104 -0.0166538988
## 90 91 92 93 94
## -0.2101998536 0.0999245294 -0.2764622533 0.1196021546 -0.1969040255
## 95 96 97 98 99
## 0.4246182427 0.0866703371 -0.2692966292 0.1022241170 0.1845049143
## 100 101 102 103 104
## 0.2844814622 0.0567238754 0.0718908996 -0.0193711583 0.3085424980
## 105 106 107 108 109
## -0.2717931726 -1.1953301375 0.6730721267 -0.1633869109 0.3155728050
## 110 111 112 113 114
## -0.0091031336 0.3984023024 0.5548959808 -1.0566851701 0.7880259146
## 115 116 117 118 119
## 0.0939056670 0.1223389249 0.0491446447 0.1406920939 -0.6743811810
## 120 121 122 123 124
## 0.3197780047 0.2157982532 -0.5256451527 0.0489862102 -1.0499510287
## 125 126 127 128 129
## 0.4394807412 0.3652649330 -0.5195959156 0.3998504377 -0.1191334670
## 130 131 132 133 134
## 0.4433747581 -0.0947424623 0.0832120425 -0.5277903645 -0.1063871747
## 135 136 137 138 139
## 0.2841217598 -0.8616391162 -0.3790968311 0.7288172894 0.5071672677
## 140 141 142 143 144
## -0.2286002821 0.0314926421 -0.6829332184 0.9703729179 -0.7449079747
## 145 146 147 148 149
## 0.2679769867 -0.3756868031 0.2328898204 0.2944174911 -0.4603615280
## 150 151 152 153 154
## -0.2255009541 -0.0717132127 -0.1898146588 0.0234792637 0.3163682613
## 155 156 157 158 159
## 0.2111669824 -0.2559877586 -0.0066921052 -0.1121490904 -0.0041986795
## 160 161 162 163 164
## 0.0424280537 0.3866164312 0.3249911181 -0.4301015712 -0.0217016916
## 165 166 167 168 169
## -0.2131773712 0.0505797912 0.0663116210 0.2714930485 0.2043053345
## 170 171 172 173 174
## -0.3305856683 0.0199390521 -0.0987236863 -0.0879896828 -0.1770255319
## 175 176 177 178 179
## 0.9075754923 -0.1057388530 -0.4752423733 -0.1321610850 -0.3801484525
## 180 181 182 183 184
## 0.5419094734 -0.2656456412 0.1227014611 0.2842934188 -0.3350889685
## 185 186 187 188 189
## 0.5033548382 -0.0068548374 -0.6091154625 -0.2503721300 0.0775616818
## 190 191 192 193 194
## 0.8245964949 -0.3712032240 -0.6583240983 1.1415074891 0.0754030017
## 195 196 197 198 199
## 0.6061736284 -0.2877254417 -0.7529277730 -0.8836332442 0.7384886742
## 200 201 202 203 204
## 0.0897824100 0.7422410308 0.3995787787 0.7494566948 0.8276606603
## 205 206 207 208 209
## 0.1200761219 -0.0654303538 -0.2230863545 0.0274122666 -0.0400149964
## 210 211 212 213 214
## 0.0022512118 0.2936783139 0.0990719213 0.0543947860 -0.0493149906
## 215 216 217 218 219
## -0.0373004111 0.3833824395 0.0185383025 0.0589516846 0.0781896085
## 220 221 222 223 224
## 0.1379129373 -0.0118587807 -0.1957035215 0.1029201034 -0.1096721278
## 225 226 227 228 229
## 0.2728494624 0.2057127592 -0.1336138055 0.0636875549 0.2787792813
## 230 231 232 233 234
## -0.0819055576 -0.2028231242 0.1279166587 0.6104019865 0.5059773785
## 235 236 237 238 239
## 0.2927907643 0.3309247297 -0.2103299644 -0.6020374951 -0.2870039810
## 240 241 242 243 244
## -0.1242200552 0.1387655073 0.1208341292 0.1154879578 -0.1883789764
## 245 246 247 248 249
## -0.1700820686 -0.4658964526 -0.8623299961 0.6775253499 0.0105449122
## 250 251 252 253 254
## -0.0087829510 0.1708893966 -0.2762265336 -0.0240055186 0.3459538609
## 255 256 257 258 259
## -0.1418843551 -0.1564006393 -0.1053706580 0.1066407105 -0.1853499335
## 260 261 262 263 264
## -0.2487433641 -0.2333642650 -0.2727303989 -0.1687733447 -0.0466078025
## 265 266 267 268 269
## -0.3995324342 -0.0677488924 -0.0471187115 -0.0601087398 -0.1041610652
## 270 271 272 273 274
## -0.2367197351 -0.3989378404 0.2484457684 -0.1568777389 -0.7453024532
## 275 276 277 278 279
## 0.3555214858 0.1002671666 -0.3868654278 0.3040895309 -0.2028461658
## 280 281 282 283 284
## 0.1722189512 -0.2332142707 -0.0440658053 -0.3086458206 -0.0504900649
## 285 286 287 288 289
## 0.1012008512 0.1700433893 -0.3481999153 -0.3257685419 0.0074100728
## 290 291 292 293 294
## 0.0341751172 -1.4888343080 -0.7335710249 -0.5480315814 0.7716219916
## 295 296 297 298 299
## -0.3682446885 -0.0486605721 -0.1022491050 0.4153375971 -0.6283894824
## 300 301 302 303 304
## 0.2012134868 -0.5205160486 -0.1192180476 -0.0939335491 0.4307161292
## 305 306 307 308 309
## -0.1346345308 -0.6418514036 -0.1222579844 0.1329938855 0.1042333559
## 310 311 312 313 314
## 0.5206664141 -0.6846115233 -0.3201812611 0.0842644910 0.6126850050
## 315 316 317 318 319
## 0.5875763431 -0.4078496593 0.2353657459 0.3752687472 0.3007912347
## 320 321 322 323 324
## 0.0219233387 -0.5585097529 0.0920338782 0.4985910974 -0.2534512110
## 325 326 327 328 329
## -0.1352546575 -0.0338617618 -1.2401356127 -0.0603990799 0.6927204590
## 330 331 332 333 334
## 0.8101645216 0.4554625066 0.2758977507 -0.1558902425 0.2324918101
## 335 336 337 338 339
## -0.1571132546 -0.3554635846 0.1720243647 -0.0368614666 -0.2860883750
## 340 341 342 343 344
## 0.3664146703 0.3245726439 -0.8113220120 0.3094211668 0.1261280314
## 345 346 347 348 349
## 0.1013780624 0.5355813115 -0.2189059879 0.4203520863 0.4150589674
## 350 351 352 353 354
## 0.3031770151 0.1136186294 0.3525790847 0.0603945804 0.6853335007
## 355 356 357 358 359
## 0.3605603211 -0.5404365110 -0.6752436627 0.5970516429 0.8297212770
## 360 361 362 363 364
## 0.7278450588 0.5652834562 0.5630755331 -0.1175717912 -0.1903461945
## 365 366 367 368 369
## 0.0972404074 0.3422963065 0.3265283580 0.0821512567 0.4221394520
## 370 371 372 373 374
## 0.3144995798 0.0242426290 -0.0869549654 0.1292901847 0.0371106374
## 375 376 377 378 379
## 0.1510399797 0.1887376894 0.2498141128 -0.1476159290 -0.2584843004
## 380 381 382 383 384
## 0.2742931587 0.3827214873 0.2861100347 0.0320705553 -0.8687612922
## 385 386 387 388 389
## -0.6717371112 0.0901594979 0.3829023442 -0.0934348061 -0.0938720504
## 390 391 392 393 394
## 0.1243421596 0.0823670432 -0.4012690476 -0.3010281636 -0.0453070090
## 395 396 397 398 399
## -0.1682664417 -0.0227266962 -0.1872004916 -0.1452224339 -0.5144250145
## 400 401 402 403 404
## -0.1922387100 -0.0878008475 -0.0624489138 -0.2762842108 0.0024621932
## 405 406 407 408 409
## -0.0521510737 -0.7394339480 0.0295910486 -0.2974149703 -0.4524329524
## 410 411 412 413 414
## -0.0942575808 -0.2679268279 -0.1104944518 -0.5897524445 0.3438203257
## 415 416 417 418 419
## -0.1288860696 -0.2150139160 -0.0303903430 0.0037787687 -0.4397751792
## 420 421 422 423 424
## -0.6832706400 -0.4453951363 -0.1344499452 -0.8179229615 -0.4643839583
## 425 426 427 428 429
## 0.5094620775 -0.3647641012 0.3028159342 0.2062176388 0.1865326352
## 430 431 432 433 434
## -0.5719646627 0.1892242928 0.0735899417 -0.4111611070 0.2540204491
## 435 436 437 438 439
## 0.0494242221 -0.5904800236 -0.1388350201 -0.1684062474 -0.1357092483
## 440 441 442 443 444
## 0.1638572878 0.4641277285 0.9046284552 -0.5630378051 -0.2394969869
## 445 446 447 448 449
## -0.1976548938 -0.2692456496 0.0486816515 0.2693518653 0.1750217782
## 450 451 452 453 454
## -0.3212230719 -0.1564946816 -0.2735179742 -0.1829370659 -0.0562354176
## 455 456 457 458 459
## 0.2751055137 0.1558797044 0.1341932450 -0.3953978283 0.2066401363
## 460 461 462 463 464
## 0.6027321415 -0.6998549402 0.0009059039 -0.0013204327 0.0471160495
## 465 466 467 468 469
## 0.3756997387 0.7391826271 -0.3535968665 -0.1872812377 -0.4631693409
## 470 471 472 473 474
## -0.4225914438 0.2121285303 0.0406720251 -0.3903567773 -0.2813712050
## 475 476 477 478 479
## -0.5980437445 1.1517746897 -0.7341497203 0.2773720907 0.3208178831
## 480 481 482 483 484
## 0.3306062548 0.3199183622 0.5542635356 -0.8634054777 -0.1105232295
## 485 486 487 488 489
## 0.2386241573 -0.0339323640 0.1725353984 -0.1361991729 0.3281013347
## 490
## -0.0849704518
exp(f_ardl92_hanover $forecasts[1,2])
## [1] 1.518537
exp(f_ardl92_hanover $forecasts[1,1])
## [1] 0.7559629
exp(f_ardl92_hanover $forecasts[1,3])
## [1] 3.25878
exp(f_ardl92_hanover $forecasts[1,2]) - exp(full_cases_wastewater_weather_data_hanover_test[1,6])
## [1] 0.4103295
exp(f_ardl92_hanover$forecasts[7,2])
## [1] 1.893468
exp(f_ardl92_hanover$forecasts[7,1])
## [1] 0.6866424
exp(f_ardl92_hanover$forecasts[7,3])
## [1] 4.932396
exp(f_ardl92_hanover$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_hanover_test[7,6])
## [1] -0.3649397
exp(f_ardl92_hanover$forecasts[14,2])
## [1] 2.281199
exp(f_ardl92_hanover$forecasts[14,1])
## [1] 0.7101495
exp(f_ardl92_hanover$forecasts[14,3])
## [1] 7.184008
exp(f_ardl92_hanover$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_hanover_test[14,6])
## [1] 1.441972
mod_ardl144_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
p=4,q=14)
summary(mod_ardl144_hanover) #wastewater is significant at current time t
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.46038 -0.20792 0.00467 0.22007 1.13810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.70777 0.23897 -2.962 0.003218 **
## log_viral_gene.t 0.08027 0.02945 2.725 0.006674 **
## log_viral_gene.1 -0.02027 0.04045 -0.501 0.616493
## log_viral_gene.2 -0.03592 0.03996 -0.899 0.369136
## log_viral_gene.3 0.03672 0.04051 0.906 0.365207
## log_viral_gene.4 -0.01029 0.02996 -0.344 0.731279
## log_mean_new_cases.1 0.42417 0.04675 9.074 < 2e-16 ***
## log_mean_new_cases.2 0.12347 0.05092 2.425 0.015700 *
## log_mean_new_cases.3 0.03161 0.05067 0.624 0.533023
## log_mean_new_cases.4 0.16856 0.05057 3.333 0.000928 ***
## log_mean_new_cases.5 0.11553 0.05096 2.267 0.023852 *
## log_mean_new_cases.6 0.10487 0.05117 2.050 0.040979 *
## log_mean_new_cases.7 0.19118 0.05140 3.719 0.000225 ***
## log_mean_new_cases.8 -0.02135 0.05163 -0.414 0.679433
## log_mean_new_cases.9 -0.06158 0.05162 -1.193 0.233514
## log_mean_new_cases.10 0.04080 0.05123 0.796 0.426224
## log_mean_new_cases.11 -0.07317 0.05054 -1.448 0.148400
## log_mean_new_cases.12 -0.17253 0.05060 -3.409 0.000709 ***
## log_mean_new_cases.13 -0.01017 0.05077 -0.200 0.841293
## log_mean_new_cases.14 0.04810 0.04652 1.034 0.301651
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3733 on 456 degrees of freedom
## Multiple R-squared: 0.9058, Adjusted R-squared: 0.9018
## F-statistic: 230.7 on 19 and 456 DF, p-value: < 2.2e-16
f_ardl144_hanover <- forecast(mod_ardl144_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl144_hanover$forecasts)
## [1] 0.3511095
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl144_hanover$forecasts)
## [1] 0.2439619
checkresiduals(mod_ardl144_hanover)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## 0.2320250133 -0.2300846268 0.0000143706 0.0349184796 0.1300112992
## 20 21 22 23 24
## 0.2269348984 0.1717666001 0.1929651664 0.0276352616 0.0080272764
## 25 26 27 28 29
## -0.0713886061 -0.2495602697 0.6592158224 -0.2817253131 0.2281100247
## 30 31 32 33 34
## -0.4411943580 0.1532365877 -0.0156566104 -0.0368831583 0.3346043139
## 35 36 37 38 39
## 0.4113480753 0.2915138018 -0.0997877747 -0.1377274602 0.1171967690
## 40 41 42 43 44
## 0.0728981131 0.1734009525 -0.2879403958 -0.3728671236 0.1890581729
## 45 46 47 48 49
## -0.1022702209 -0.0827927705 -0.2529601975 0.1074346433 -0.4642147723
## 50 51 52 53 54
## 0.1892439249 -0.1057709383 -0.3241490111 0.3878422125 -0.1495403100
## 55 56 57 58 59
## 0.1900141135 0.4615531246 0.3511700964 0.0720535093 -0.0091372757
## 60 61 62 63 64
## 0.1585805658 0.0627268763 0.2426052785 -0.0166373358 -0.2292515413
## 65 66 67 68 69
## -0.4744973309 0.6008862571 0.2073200738 0.2291873909 -0.1416975454
## 70 71 72 73 74
## 0.5162789631 0.0382342363 -0.0139391476 0.1244000009 -0.1324811504
## 75 76 77 78 79
## 0.1806257338 0.3842008718 0.1482590155 0.1888318873 0.2084414841
## 80 81 82 83 84
## 0.4442406183 0.2583154205 0.1566341352 -0.0632220448 -0.1780292972
## 85 86 87 88 89
## 0.1621321007 -0.0922429867 0.1587955484 -0.3455528342 -0.0183598240
## 90 91 92 93 94
## -0.2600593310 0.0838163904 -0.2549937596 0.1889810200 -0.1407017110
## 95 96 97 98 99
## 0.3930241521 0.1118718051 -0.2078136487 0.1732990744 0.2469364644
## 100 101 102 103 104
## 0.2710655412 0.0661076090 0.1018750162 0.0054691777 0.3025625885
## 105 106 107 108 109
## -0.2917380929 -1.2157419496 0.6787783795 -0.1665914037 0.1909557743
## 110 111 112 113 114
## -0.0118667727 0.4722382175 0.6537192716 -0.9720931974 0.8171383491
## 115 116 117 118 119
## 0.2040302630 0.1837301425 -0.0368683171 -0.0199302637 -0.6525793571
## 120 121 122 123 124
## 0.3254338513 0.1973811120 -0.5357641822 0.1292569313 -1.0387411914
## 125 126 127 128 129
## 0.2443203713 0.3406920104 -0.3873295459 0.4437870875 -0.0110202004
## 130 131 132 133 134
## 0.5014494882 -0.1170924538 0.1757481459 -0.3335584158 -0.0533921273
## 135 136 137 138 139
## 0.2212596638 -1.0139588858 -0.3790866848 0.7811903992 0.4771799052
## 140 141 142 143 144
## -0.2222172829 0.1247146408 -0.5937242123 0.9887303643 -0.6838390958
## 145 146 147 148 149
## 0.2061571359 -0.3248286803 0.2071951389 0.1451888846 -0.5530813689
## 150 151 152 153 154
## -0.0966200035 0.0725994322 -0.2369505679 -0.0935440009 0.3477337301
## 155 156 157 158 159
## 0.3082097594 -0.2227478650 0.0252603792 -0.1180233746 0.0527919414
## 160 161 162 163 164
## 0.0812329174 0.3045683433 0.2702736226 -0.4723402109 -0.0742506942
## 165 166 167 168 169
## -0.1516700072 0.1084299846 0.1099269486 0.1543529346 0.1500562454
## 170 171 172 173 174
## -0.3690503180 -0.0205702751 -0.0804764764 -0.0125241231 -0.1551577888
## 175 176 177 178 179
## 0.8063617348 -0.0780030506 -0.5291281104 -0.1372098955 -0.3568820576
## 180 181 182 183 184
## 0.5876690665 -0.2302114632 0.0426042038 0.1276556525 -0.3711892151
## 185 186 187 188 189
## 0.3821713998 0.0276806120 -0.3800235232 -0.2661621638 -0.0798252779
## 190 191 192 193 194
## 0.7329291365 -0.3894195176 -0.5834256981 1.1380973689 0.0705385167
## 195 196 197 198 199
## 0.5712203719 -0.3233007880 -0.6890275589 -0.9318087445 0.4993778499
## 200 201 202 203 204
## -0.1129632849 0.7596497156 0.5279075014 0.6634235694 0.7060288938
## 205 206 207 208 209
## 0.2728171372 0.0623981186 -0.1525779449 -0.0898095995 -0.4107703365
## 210 211 212 213 214
## -0.3803512438 0.1549021151 0.0686055849 0.0310103853 -0.0764072753
## 215 216 217 218 219
## 0.0140504236 0.4216517065 -0.0034951842 -0.0075872257 0.0454263630
## 220 221 222 223 224
## 0.1093738013 -0.0568475137 -0.2096177809 0.1098621148 -0.1215136008
## 225 226 227 228 229
## 0.2041466416 0.1491517355 -0.1573109650 0.0925667395 0.3201375162
## 230 231 232 233 234
## -0.0932453663 -0.1914384460 0.1150312084 0.5861666964 0.4695548625
## 235 236 237 238 239
## 0.2970770151 0.3010274480 -0.1672028795 -0.6178253411 -0.3075969303
## 240 241 242 243 244
## -0.2082358348 0.1082555938 0.0397408411 -0.0781370906 -0.1812830250
## 245 246 247 248 249
## -0.0715619905 -0.2950765747 -0.7991340757 0.7493444370 0.0277891587
## 250 251 252 253 254
## -0.1000750479 0.1961736231 -0.1532057808 0.0561568517 0.4509695586
## 255 256 257 258 259
## -0.0561706886 -0.1106163370 -0.1063070571 -0.0123132162 -0.2773329012
## 260 261 262 263 264
## -0.1739023622 -0.1372940145 -0.2603351082 -0.1856692693 -0.1100029435
## 265 266 267 268 269
## -0.4053952517 0.0124290030 0.0669362304 -0.0220836887 -0.0375369249
## 270 271 272 273 274
## -0.1419381642 -0.3607986817 0.2681801439 -0.1215579572 -0.7396969867
## 275 276 277 278 279
## 0.3697099511 0.1293586740 -0.4011285781 0.3328928730 -0.1165749959
## 280 281 282 283 284
## 0.2297345452 -0.2299800115 -0.0608823386 -0.3267949361 -0.0025010517
## 285 286 287 288 289
## 0.0644444196 0.0701412964 -0.2968815121 -0.2653501889 -0.0152858289
## 290 291 292 293 294
## 0.0558851139 -1.4603755107 -0.7648996770 -0.5913572414 0.7002986103
## 295 296 297 298 299
## -0.3741254843 -0.0057037782 0.0762723113 0.5929471875 -0.5500160748
## 300 301 302 303 304
## 0.2730759101 -0.3205410948 -0.0428166695 -0.2941196006 0.2210274224
## 305 306 307 308 309
## -0.1295237034 -0.5021145770 -0.0837131735 0.1156441659 0.0198313147
## 310 311 312 313 314
## 0.5430597700 -0.7234020154 -0.3205984478 0.0696901478 0.5436954910
## 315 316 317 318 319
## 0.6062876647 -0.1745014570 0.2708071071 0.2894306578 0.2210611394
## 320 321 322 323 324
## 0.0472606162 -0.4833797089 0.1025954041 0.3285643577 -0.5241406006
## 325 326 327 328 329
## -0.2634225673 0.0492345286 -1.2091492452 -0.2276069145 0.5956708340
## 330 331 332 333 334
## 0.8159789018 0.5102077200 0.3134650203 -0.1604034240 0.3051622425
## 335 336 337 338 339
## -0.0616198104 -0.3842638935 0.1145812366 -0.1926680658 -0.6270725788
## 340 341 342 343 344
## 0.1795970159 0.3023288005 -0.6475701299 0.3273887520 0.2354417156
## 345 346 347 348 349
## 0.0083160036 0.5343726003 -0.1930468830 0.4622699905 0.5427911877
## 350 351 352 353 354
## 0.3218424245 0.0209946864 0.3504951811 0.0281858198 0.5289258297
## 355 356 357 358 359
## 0.3076804536 -0.5669043519 -0.7399932806 0.4920667410 0.6732596071
## 360 361 362 363 364
## 0.6530432962 0.5873000138 0.6125703814 -0.1179175164 -0.2253975234
## 365 366 367 368 369
## 0.0649561480 0.3775535042 0.2841923641 -0.1915909893 0.1343152552
## 370 371 372 373 374
## 0.2501988565 0.1193298318 0.0036778451 0.2056891041 0.0434580953
## 375 376 377 378 379
## -0.0076332665 0.0038717271 0.2096826562 -0.0666120484 -0.2222461427
## 380 381 382 383 384
## 0.2688187193 0.4132895302 0.3098874051 -0.0048492087 -0.8733770573
## 385 386 387 388 389
## -0.6706971117 0.1095052226 0.3587255761 -0.0425208246 -0.0185968557
## 390 391 392 393 394
## 0.1176113655 0.0793784585 -0.2832013293 -0.1451613476 0.1382852449
## 395 396 397 398 399
## -0.1223831004 -0.1669238330 -0.3279819878 -0.0800620886 -0.3394125607
## 400 401 402 403 404
## -0.0892425084 -0.0323232762 0.0287631448 -0.2193074140 -0.0128360581
## 405 406 407 408 409
## 0.0108395011 -0.6106048622 0.0824733859 -0.2087651664 -0.3972848782
## 410 411 412 413 414
## -0.0651620460 -0.3015389795 -0.0820667767 -0.4796685020 0.4414204728
## 415 416 417 418 419
## -0.0343043217 -0.0857207655 0.0584775152 0.0010112751 -0.3548307299
## 420 421 422 423 424
## -0.6124304550 -0.4652583067 -0.1293264643 -0.8053766443 -0.5002958966
## 425 426 427 428 429
## 0.4688260419 -0.2401283857 0.4179923558 0.3093850326 0.3576574681
## 430 431 432 433 434
## -0.3958215691 0.2340110628 0.0634697767 -0.3865980684 0.2745122858
## 435 436 437 438 439
## -0.1218894973 -0.6588760861 -0.1129545478 -0.2027723541 -0.1701413701
## 440 441 442 443 444
## 0.2246033620 0.4941633337 0.8351275584 -0.4641952110 -0.1636153485
## 445 446 447 448 449
## -0.2019021139 -0.1736399643 0.0362359011 0.1788713562 0.0350802184
## 450 451 452 453 454
## -0.3625821869 -0.2257768002 -0.3004671611 -0.0152157890 0.0537056711
## 455 456 457 458 459
## 0.1963532056 0.0377203338 0.1115567708 -0.4189798654 0.2197457705
## 460 461 462 463 464
## 0.7445384771 -0.6453127672 -0.0864044489 -0.1265151657 -0.0414112259
## 465 466 467 468 469
## 0.2635374263 0.7002040516 -0.2519372951 -0.1744044534 -0.5277812710
## 470 471 472 473 474
## -0.5665540620 0.1907896541 0.0679088360 -0.5417137734 -0.4195097311
## 475 476 477 478 479
## -0.6749111453 1.0782110734 -0.6108349490 0.4326265163 0.3875669153
## 480 481 482 483 484
## 0.2650572381 0.2321079461 0.5394385073 -0.7497957365 -0.0738481523
## 485 486 487 488 489
## 0.1564739115 -0.2600493119 0.0135448991 -0.1512259159 0.2095058645
## 490
## -0.1656435051
mod_ardl113_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
p=13,q=1)
f_ardl113_hanover <- forecast(mod_ardl113_hanover, x= t(full_cases_wastewater_weather_data_hanover_test[,7]),h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl113_hanover$forecasts)
## [1] 0.4558737
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl113_hanover$forecasts)
## [1] 0.3146763
checkresiduals(mod_ardl113_hanover)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## 2.464235e-01 1.079214e-01 -3.004630e-01 1.146269e-01 1.634199e-01
## 19 20 21 22 23
## 2.233038e-01 2.089266e-01 1.961528e-01 2.025143e-01 -8.934657e-02
## 24 25 26 27 28
## -1.165070e-04 4.644103e-02 -1.229424e-01 8.704921e-01 -3.485893e-01
## 29 30 31 32 33
## 4.296294e-01 -5.434006e-01 4.591188e-01 2.953427e-02 7.280774e-02
## 34 35 36 37 38
## 4.296377e-01 4.310221e-01 1.366181e-01 -2.663207e-01 2.369030e-02
## 39 40 41 42 43
## 2.993593e-01 1.616120e-01 3.200558e-01 -1.097091e-01 -1.771500e-01
## 44 45 46 47 48
## 2.759151e-01 -5.614891e-02 -1.513982e-02 -2.425796e-01 2.745084e-01
## 49 50 51 52 53
## -3.950627e-01 4.078371e-01 -1.848751e-01 -3.081471e-01 4.125180e-01
## 54 55 56 57 58
## -2.619204e-01 3.928730e-01 2.722821e-01 1.957764e-01 -1.152038e-01
## 59 60 61 62 63
## -3.133690e-02 2.275582e-01 1.220873e-01 4.100802e-01 1.097825e-01
## 64 65 66 67 68
## -3.351586e-02 -1.332685e-01 9.242413e-01 1.932721e-01 1.574233e-01
## 69 70 71 72 73
## -1.507731e-01 5.909563e-01 -6.515428e-02 5.172955e-02 3.029702e-01
## 74 75 76 77 78
## -2.456603e-04 3.266876e-01 3.205375e-01 3.190554e-01 8.812246e-02
## 79 80 81 82 83
## -4.173743e-02 5.607035e-01 2.586454e-01 1.669316e-01 1.679341e-01
## 84 85 86 87 88
## 9.005550e-02 4.301698e-01 -2.036480e-02 4.957941e-01 -3.665758e-01
## 89 90 91 92 93
## 2.342454e-01 -9.673563e-02 4.142025e-01 -2.138409e-01 1.517826e-01
## 94 95 96 97 98
## -1.757819e-01 4.942384e-01 -2.824774e-05 -2.657460e-01 3.263593e-01
## 99 100 101 102 103
## 2.360464e-01 1.843038e-01 2.402811e-02 9.507516e-02 7.453924e-03
## 104 105 106 107 108
## 4.273160e-01 -2.532310e-01 -9.490978e-01 1.245190e+00 -2.651686e-01
## 109 110 111 112 113
## 4.272234e-01 -1.886624e-01 5.328153e-01 3.786976e-01 -1.321191e+00
## 114 115 116 117 118
## 1.371759e+00 3.410164e-02 1.787187e-01 -6.101586e-02 3.204270e-01
## 119 120 121 122 123
## -5.790502e-01 4.839995e-01 3.184289e-01 -4.041732e-01 1.807141e-01
## 124 125 126 127 128
## -9.884007e-01 9.774889e-01 2.090924e-01 -4.622352e-01 7.442776e-01
## 129 130 131 132 133
## -3.064776e-01 5.737385e-01 -4.162272e-01 3.752668e-01 -5.122829e-01
## 134 135 136 137 138
## 5.545539e-02 5.186287e-01 -9.418320e-01 -2.106306e-03 8.818772e-01
## 139 140 141 142 143
## 1.984605e-01 -5.242476e-01 3.891965e-02 -5.926545e-01 1.123021e+00
## 144 145 146 147 148
## -1.052675e+00 6.892360e-01 -4.172753e-01 2.450462e-01 1.571643e-01
## 149 150 151 152 153
## -3.432682e-01 1.542178e-02 4.661517e-02 -1.400209e-01 8.230218e-02
## 154 155 156 157 158
## 2.741594e-01 5.706222e-02 -5.145570e-01 6.245565e-02 -7.761043e-02
## 159 160 161 162 163
## 1.199057e-01 3.838372e-02 5.091085e-01 1.678180e-01 -8.170937e-01
## 164 165 166 167 168
## 1.118598e-01 -1.518930e-01 1.779649e-01 9.953022e-02 2.616328e-01
## 169 170 171 172 173
## 1.053195e-01 -3.941159e-01 9.659943e-03 8.265184e-02 9.181983e-03
## 174 175 176 177 178
## -1.691638e-01 8.420499e-01 -4.279412e-01 -5.868518e-01 -2.490959e-01
## 179 180 181 182 183
## -2.433995e-01 6.580741e-01 -4.743333e-01 1.144835e-01 1.151714e-01
## 184 185 186 187 188
## -5.545354e-01 5.834953e-01 -2.632818e-01 -4.661061e-01 -2.926448e-01
## 189 190 191 192 193
## 1.405434e-01 6.479839e-01 -9.255004e-01 -5.008435e-01 1.184592e+00
## 194 195 196 197 198
## -3.517067e-01 4.503288e-01 -8.232858e-01 -4.901369e-01 -8.238246e-01
## 199 200 201 202 203
## 8.034251e-01 3.499138e-02 5.298002e-01 -1.900180e-01 3.388748e-01
## 204 205 206 207 208
## 3.008035e-01 -2.647209e-01 5.605422e-02 -1.561656e-01 2.706322e-01
## 209 210 211 212 213
## -6.116054e-02 -1.520668e-02 2.902518e-01 -7.375718e-02 -1.946204e-02
## 214 215 216 217 218
## -1.101271e-01 5.860545e-02 3.933577e-01 -2.067138e-01 6.567620e-02
## 219 220 221 222 223
## 2.240577e-02 1.117048e-01 -1.444287e-01 -1.224293e-01 2.235235e-01
## 224 225 226 227 228
## -1.992278e-01 2.591305e-01 9.701836e-02 -1.741103e-01 7.201539e-03
## 229 230 231 232 233
## 2.818788e-01 -1.599871e-01 -2.520877e-01 1.892706e-01 6.324726e-01
## 234 235 236 237 238
## 3.566457e-01 5.142079e-02 2.829246e-01 -2.928293e-01 -4.235424e-01
## 239 240 241 242 243
## 1.088054e-01 2.086854e-01 2.177394e-01 2.340707e-01 -4.925637e-02
## 244 245 246 247 248
## -1.978960e-01 -3.000210e-02 -1.177888e-01 -5.652781e-01 7.513701e-01
## 249 250 251 252 253
## -3.479821e-02 -2.405153e-01 4.745448e-02 -2.752346e-01 1.505968e-01
## 254 255 256 257 258
## 3.619144e-01 -1.689926e-01 -1.230290e-01 -1.604969e-01 1.582474e-01
## 259 260 261 262 263
## -1.624001e-01 -2.088017e-01 -3.651384e-02 -3.797311e-02 -9.440940e-02
## 264 265 266 267 268
## 9.062343e-03 -3.950558e-01 4.795182e-02 -1.088870e-01 -9.442184e-02
## 269 270 271 272 273
## -1.839960e-01 -2.549597e-01 -3.852999e-01 3.209049e-01 -3.319555e-01
## 274 275 276 277 278
## -7.272679e-01 5.069109e-01 -1.457574e-01 -5.504818e-01 2.266118e-01
## 279 280 281 282 283
## -3.179506e-01 2.094433e-01 -5.519211e-01 1.078107e-01 -1.970213e-01
## 284 285 286 287 288
## -5.879788e-02 9.916075e-02 6.117743e-02 -4.252216e-01 -3.849268e-01
## 289 290 291 292 293
## 8.777387e-02 1.012035e-01 -1.544862e+00 -2.378311e-01 -2.628968e-01
## 294 295 296 297 298
## 9.015871e-01 -8.794420e-01 -1.230085e-01 -3.705736e-01 1.706511e-01
## 299 300 301 302 303
## -1.020351e+00 3.866089e-01 -5.547021e-01 -1.056843e-01 -3.334892e-01
## 304 305 306 307 308
## 3.164453e-01 -4.360064e-01 -8.882716e-01 2.548828e-02 2.294604e-01
## 309 310 311 312 313
## -1.025422e-01 4.121399e-01 -7.206442e-01 -1.777182e-01 4.246002e-02
## 314 315 316 317 318
## 5.876482e-01 5.512028e-01 -8.205486e-01 2.313312e-01 1.723283e-01
## 319 320 321 322 323
## 1.575748e-01 -7.467539e-02 -4.518359e-01 1.045983e-01 4.637128e-01
## 324 325 326 327 328
## -4.974163e-01 -3.237650e-01 -8.134881e-02 -1.279873e+00 2.623930e-01
## 329 330 331 332 333
## 6.861806e-01 6.039959e-01 -1.893753e-01 -2.304746e-01 -3.635442e-01
## 334 335 336 337 338
## 1.131718e-01 -1.675207e-01 -6.220534e-02 3.617296e-01 -1.905118e-01
## 339 340 341 342 343
## -3.644422e-01 5.003083e-01 1.981548e-01 -8.621920e-01 7.472343e-01
## 344 345 346 347 348
## 2.326173e-01 -9.845740e-03 -3.949285e-02 -1.092496e-01 3.196866e-01
## 349 350 351 352 353
## 1.918624e-01 1.899830e-01 2.726169e-01 3.127908e-01 -3.066221e-01
## 354 355 356 357 358
## 5.910136e-01 1.965529e-01 -6.071190e-01 -4.901459e-01 9.571559e-01
## 359 360 361 362 363
## 7.785486e-01 4.297194e-01 2.421168e-01 3.839082e-01 -4.124742e-01
## 364 365 366 367 368
## -1.594592e-01 5.397143e-01 6.824647e-01 3.062328e-01 -9.025481e-02
## 369 370 371 372 373
## 4.896963e-01 1.661832e-01 -1.106755e-01 1.151560e-01 4.256767e-01
## 374 375 376 377 378
## 1.514870e-01 1.344179e-01 2.897561e-01 3.059985e-01 -2.154945e-01
## 379 380 381 382 383
## -1.121419e-01 5.715364e-01 5.037337e-01 2.597667e-01 2.678688e-03
## 384 385 386 387 388
## -7.643494e-01 -2.123807e-01 5.206294e-01 6.137937e-01 -1.848080e-01
## 389 390 391 392 393
## -5.785141e-02 7.055641e-02 1.484102e-02 -3.839321e-01 9.331012e-02
## 394 395 396 397 398
## 3.080681e-01 -1.100519e-01 1.106134e-02 -1.627662e-01 -5.214472e-02
## 399 400 401 402 403
## -3.746169e-01 1.083442e-02 8.842576e-02 3.438985e-02 -2.792617e-01
## 404 405 406 407 408
## 3.434635e-02 -5.540646e-02 -7.308652e-01 2.899233e-01 -2.045589e-01
## 409 410 411 412 413
## -2.821170e-01 -6.731756e-03 -2.594225e-01 -6.360104e-02 -5.690875e-01
## 414 415 416 417 418
## 5.139666e-01 -2.785183e-01 -2.416842e-01 2.851707e-03 -5.649891e-02
## 419 420 421 422 423
## -4.842228e-01 -5.641338e-01 -1.314034e-01 5.936359e-02 -8.771841e-01
## 424 425 426 427 428
## -2.356548e-01 5.635040e-01 -7.011404e-01 2.578767e-01 -9.083970e-02
## 429 430 431 432 433
## 8.442828e-02 -8.394920e-01 2.948416e-01 9.040904e-02 -5.392915e-01
## 434 435 436 437 438
## 3.089598e-01 -1.191922e-01 -6.222080e-01 6.719370e-02 -1.150110e-01
## 439 440 441 442 443
## 3.532734e-02 4.811247e-02 4.837361e-01 5.586254e-01 -1.049955e+00
## 444 445 446 447 448
## 4.864179e-02 -6.837657e-02 1.778991e-03 1.089735e-01 2.395360e-01
## 449 450 451 452 453
## 3.266427e-03 -6.188671e-01 1.802997e-03 -3.534254e-01 1.084297e-01
## 454 455 456 457 458
## -8.825934e-02 6.616639e-02 -1.929277e-01 -1.725775e-01 -4.585026e-01
## 459 460 461 462 463
## 1.243172e-01 6.099323e-01 -1.027856e+00 -3.668340e-02 -1.753207e-01
## 464 465 466 467 468
## -1.369623e-03 2.937642e-01 4.236799e-01 -5.605061e-01 -4.239888e-01
## 469 470 471 472 473
## -6.300182e-01 -2.718373e-01 3.205351e-01 4.337715e-02 -6.084656e-01
## 474 475 476 477 478
## -3.567059e-01 -7.152771e-01 1.130024e+00 -1.263828e+00 4.330856e-01
## 479 480 481 482 483
## -2.140565e-02 4.015963e-02 -1.016249e-01 2.597769e-01 -1.023427e+00
## 484 485 486 487 488
## 1.045923e-02 2.361395e-01 1.646838e-02 4.290089e-02 -3.014100e-01
## 489 490
## 3.222930e-01 -3.431487e-01
mod_ardl51_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
p=1,q=5)
f_ardl51_hanover <- forecast(mod_ardl51_hanover, x= t(full_cases_wastewater_weather_data_hanover_test[,7]),h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl51_hanover$forecasts)
## [1] 0.3492377
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl51_hanover$forecasts)
## [1] 0.2607468
checkresiduals(mod_ardl51_hanover)
## Time Series:
## Start = 6
## End = 490
## Frequency = 1
## 6 7 8 9 10
## 0.0328220635 0.0763639764 0.0046540748 -0.2435933565 -0.2577974163
## 11 12 13 14 15
## 0.0516759042 0.2088724684 0.0514321076 0.2379440878 0.1355477060
## 16 17 18 19 20
## -0.3404018235 -0.0762795959 0.0181905028 0.1338161858 0.2168810809
## 21 22 23 24 25
## 0.2438434500 0.2303942844 -0.0762856882 -0.0914221855 -0.1075191351
## 26 27 28 29 30
## -0.2528528180 0.6965248952 -0.1966205776 0.3446781039 -0.4866767653
## 31 32 33 34 35
## 0.1234975029 -0.1079042044 -0.0359000648 0.3911615870 0.3984112673
## 36 37 38 39 40
## 0.2589576236 -0.1825436274 -0.2006553270 0.0230820382 0.0343408531
## 41 42 43 44 45
## 0.2670376906 -0.1516682173 -0.2924471169 0.1663005442 -0.1483611933
## 46 47 48 49 50
## -0.1304079347 -0.3038889904 0.1123624375 -0.4812507250 0.2015047254
## 51 52 53 54 55
## -0.1167572451 -0.3905704203 0.2873605917 -0.2100333373 0.1991205844
## 56 57 58 59 60
## 0.3377884608 0.2878576352 -0.0112247739 -0.1244478406 0.1350154484
## 61 62 63 64 65
## 0.0195464901 0.2220958294 0.1528199852 -0.1264946905 -0.4535805420
## 66 67 68 69 70
## 0.6484584361 0.2054829326 0.2050423000 -0.1984259567 0.4654973111
## 71 72 73 74 75
## -0.0671907248 -0.1283758975 0.1797225951 -0.0835458903 0.1659951176
## 76 77 78 79 80
## 0.4490215584 0.2860305338 0.1319700286 0.0588109250 0.4287021695
## 81 82 83 84 85
## 0.2943369054 0.1532665521 0.0345187105 -0.0896816612 0.2144690016
## 86 87 88 89 90
## -0.0330599322 0.2560337493 -0.3321519426 0.0162492878 -0.2455974734
## 91 92 93 94 95
## 0.0801445848 -0.2584900654 0.1513020956 -0.1939918082 0.3837230463
## 96 97 98 99 100
## 0.0547884287 -0.2599072375 0.1123651047 0.1804603978 0.2614960953
## 101 102 103 104 105
## 0.0424809710 0.1340920949 -0.0143607607 0.2352550159 -0.2827483060
## 106 107 108 109 110
## -1.1302809975 0.7432318166 -0.1589489130 0.3097466678 0.0061081782
## 111 112 113 114 115
## 0.4755997916 0.4218489023 -1.2412130845 0.8894642542 0.1736875469
## 116 117 118 119 120
## 0.1196716528 0.0347390041 0.2573019650 -0.6944435121 0.1391592637
## 121 122 123 124 125
## 0.3016683552 -0.3959176803 0.0386666617 -1.0500290453 0.4497152879
## 126 127 128 129 130
## 0.2709627709 -0.4689198507 0.5111916380 -0.1142953724 0.3496322443
## 131 132 133 134 135
## -0.2676530964 0.1659780716 -0.4463626784 -0.1615703017 0.3017713966
## 136 137 138 139 140
## -0.8354819509 -0.3468889952 0.7393470192 0.4974614391 -0.3100390034
## 141 142 143 144 145
## 0.0453809400 -0.6179847621 0.8259374456 -0.8408228200 0.4631916712
## 146 147 148 149 150
## -0.2557795324 0.1866542614 0.1614221641 -0.4652713135 -0.1117735812
## 151 152 153 154 155
## -0.0897062933 -0.1924181773 0.0226829068 0.3536784389 0.2363930413
## 156 157 158 159 160
## -0.3703972094 -0.0597533758 -0.1111394618 -0.0085813883 0.0810836576
## 161 162 163 164 165
## 0.4954513349 0.3539532550 -0.5172433285 -0.0772402324 -0.2123895983
## 166 167 168 169 170
## 0.0412792389 0.0998877245 0.3862955862 0.2373448586 -0.4322589371
## 171 172 173 174 175
## -0.0303939708 -0.0931697330 -0.0706835758 -0.1114414152 0.9950390355
## 176 177 178 179 180
## -0.1180735463 -0.5891843459 -0.1791672014 -0.3778223779 0.5000949208
## 181 182 183 184 185
## -0.2403171841 0.3304621890 0.2767205452 -0.4924510443 0.4477556802
## 186 187 188 189 190
## 0.0338469806 -0.5087339694 -0.2582943953 0.0924207559 0.8144005047
## 191 192 193 194 195
## -0.4694046635 -0.5870480959 1.1817338961 -0.0663642675 0.5162535719
## 196 197 198 199 200
## -0.1963151678 -0.5703242741 -1.0192284376 0.6393847394 0.2537494702
## 201 202 203 204 205
## 0.8574209983 0.4158236599 0.6861549014 0.5641520776 -0.0556441121
## 206 207 208 209 210
## 0.0430313653 -0.0584692632 0.1210961054 -0.0146338842 0.0663894756
## 211 212 213 214 215
## 0.3647957113 0.0620367654 0.0126981338 -0.0629523636 -0.0214430243
## 216 217 218 219 220
## 0.3739499841 0.0210694328 0.1062839461 0.0850358761 0.1175722167
## 221 222 223 224 225
## -0.0533164168 -0.1874940075 0.1660401040 -0.0985299622 0.2591326220
## 226 227 228 229 230
## 0.2117532430 -0.1059687208 0.0377909043 0.2411376445 -0.0961667197
## 231 232 233 234 235
## -0.2048006383 0.1738253734 0.6435909589 0.4480211087 0.2890974155
## 236 237 238 239 240
## 0.3713733345 -0.2365013068 -0.6876393609 -0.2439062348 0.0227495601
## 241 242 243 244 245
## 0.1902827515 0.1370390454 0.1523487339 -0.2253344260 -0.2996517418
## 246 247 248 249 250
## -0.4934033040 -0.7875744072 0.7399061986 0.0190299083 -0.0122580201
## 251 252 253 254 255
## 0.1331211585 -0.3163738216 -0.1568586438 0.2728530752 0.0084326031
## 256 257 258 259 260
## -0.0769932479 -0.1323585306 0.0766517618 -0.2622427898 -0.2515168055
## 261 262 263 264 265
## -0.1449868382 -0.2321509216 -0.1946487051 -0.0551976273 -0.3729364222
## 266 267 268 269 270
## -0.0884180350 -0.0865935053 -0.0740020480 -0.1334970730 -0.2459930128
## 271 272 273 274 275
## -0.4058163914 0.2160045901 -0.1650742124 -0.7230092920 0.3788789122
## 276 277 278 279 280
## 0.0929187302 -0.4541820485 0.2670271838 -0.1430614311 0.1394456484
## 281 282 283 284 285
## -0.3536265863 0.0412371834 -0.2532950550 -0.0909616854 0.1136030094
## 286 287 288 289 290
## 0.1921190592 -0.3576088467 -0.3550758314 -0.0036586868 0.0114470325
## 291 292 293 294 295
## -1.5021921163 -0.6387346274 -0.4675440103 0.7314566640 -0.4452319213
## 296 297 298 299 300
## 0.0519783156 -0.1029909175 0.1687274339 -0.8368689202 0.2881969954
## 301 302 303 304 305
## -0.3417564521 -0.1160738439 -0.1781694699 0.4635169687 -0.1511082997
## 306 307 308 309 310
## -0.7198262187 -0.1252055853 0.1585814134 0.0692909369 0.5557826817
## 311 312 313 314 315
## -0.5724581013 -0.3128230661 -0.0608994764 0.5918868466 0.6246861981
## 316 317 318 319 320
## -0.3289664769 0.2875034611 0.2292978657 0.1256699915 0.0191685548
## 321 322 323 324 325
## -0.3565629427 0.2074376511 0.3895778871 -0.2960922985 -0.0717127981
## 326 327 328 329 330
## 0.0179695289 -1.2714008365 -0.1175043675 0.7699542761 0.9086689033
## 331 332 333 334 335
## 0.3913370882 0.2526266045 -0.2293985609 -0.0127086489 -0.2079899666
## 336 337 338 339 340
## -0.1131232513 0.3838826059 0.0001213912 -0.3870008513 0.3150498318
## 341 342 343 344 345
## 0.3355352127 -0.7807368899 0.3350029154 0.2243567794 0.0781485534
## 346 347 348 349 350
## 0.3951910501 -0.2000113618 0.4411837609 0.3018906571 0.3190622020
## 351 352 353 354 355
## 0.1619486336 0.3764302200 0.0607116638 0.6370763030 0.3811565810
## 356 357 358 359 360
## -0.4795675581 -0.6546619406 0.6235711231 0.8334980436 0.7380326679
## 361 362 363 364 365
## 0.6604429889 0.6014188033 -0.3349478513 -0.3809135054 0.2144427547
## 366 367 368 369 370
## 0.5667367625 0.4401506055 0.1364290666 0.4303700782 0.1739142587
## 371 372 373 374 375
## -0.1113166631 -0.0391171104 0.2789485599 0.0984224275 0.1291849204
## 376 377 378 379 380
## 0.2113764973 0.2605952310 -0.2045349577 -0.2756622538 0.3269035614
## 381 382 383 384 385
## 0.4038043635 0.2843100537 0.0634219566 -0.8326422316 -0.7345135525
## 386 387 388 389 390
## 0.0358368324 0.4625133743 0.0124788708 -0.0262299298 0.0809615424
## 391 392 393 394 395
## -0.1336994032 -0.5539679182 -0.1992215662 0.1302209005 -0.1510501884
## 396 397 398 399 400
## -0.0639693978 -0.1713004899 -0.1639580458 -0.6105724450 -0.1975370198
## 401 402 403 404 405
## -0.0214919389 -0.0493713098 -0.2997190318 -0.0023490470 -0.0974532642
## 406 407 408 409 410
## -0.8224190622 0.0266993747 -0.2308880999 -0.4371940364 -0.1164118077
## 411 412 413 414 415
## -0.2275735298 -0.1308310735 -0.6980065485 0.3727645512 -0.1157955898
## 416 417 418 419 420
## -0.2737999656 -0.0531834707 0.0192993999 -0.4943486455 -0.7445203183
## 421 422 423 424 425
## -0.3543762177 -0.0757218418 -0.8671141109 -0.4287120683 0.5694277034
## 426 427 428 429 430
## -0.4445397746 0.1713955501 0.2027104232 0.2147761718 -0.7227408330
## 431 432 433 434 435
## 0.1546070989 0.1795745860 -0.4470909945 0.2458108177 0.1368398795
## 436 437 438 439 440
## -0.5883129073 -0.2376174611 -0.1186835791 -0.0603621476 0.1022441687
## 441 442 443 444 445
## 0.5087521282 0.9328888879 -0.6850991824 -0.2844535286 -0.1935423103
## 446 447 448 449 450
## -0.2625154669 0.0435433877 0.4215548170 0.2955986368 -0.4687384889
## 451 452 453 454 455
## -0.2531259777 -0.2658642119 -0.1838665549 -0.0307415923 0.3798346395
## 456 457 458 459 460
## 0.1777119377 0.0195442935 -0.4597632990 0.2016805926 0.5829627307
## 461 462 463 464 465
## -0.7078806473 0.0767206788 0.0507332791 0.0002578649 0.2928540310
## 466 467 468 469 470
## 0.8311943554 -0.2669171559 -0.3177463592 -0.5377698565 -0.3955878865
## 471 472 473 474 475
## 0.2222802539 0.1631996470 -0.2452567405 -0.3212481852 -0.7211024806
## 476 477 478 479 480
## 1.0562259546 -0.7695242988 0.4030654240 0.3858950782 0.2753018234
## 481 482 483 484 485
## 0.1305945402 0.5064635684 -0.7354071492 -0.1479216905 0.2244361081
## 486 487 488 489 490
## 0.0604289165 0.2062820948 -0.0692500089 0.3670844588 -0.2341416187
lowest_rmse_weather_hanover <- Inf
best_mod_weather_hanover <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
remove <- list(p =list(mean_precipation = c(1:p),
mean_temp= c(1:p)))
mod <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
mean_temp,data = full_cases_wastewater_weather_data_hanover_train,
p=p,q=q,
remove = remove)
f <- forecast(mod,
x= t(full_cases_wastewater_weather_data_hanover_test[,c(7,4,5)]),
h=14)
forecast_acc <- rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f$forecasts) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_weather_hanover){
lowest_rmse_weather_hanover <- forecast_acc
best_mod_weather_hanover <- mod
}
}
}
lowest_rmse_weather_hanover #0.35
## [1] 0.3558231
summary(best_mod_weather_hanover) #ARDL(9,14) (lowest RMSE), ARDL(14,14) (lowest MAE)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.44868 -0.20312 -0.00174 0.24075 1.06440
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4196023 0.2826546 -1.485 0.13838
## log_viral_gene.t 0.0899460 0.0306394 2.936 0.00350 **
## log_viral_gene.1 -0.0165224 0.0415725 -0.397 0.69123
## log_viral_gene.2 -0.0498911 0.0415549 -1.201 0.23054
## log_viral_gene.3 0.0439677 0.0423291 1.039 0.29950
## log_viral_gene.4 0.0578390 0.0424261 1.363 0.17347
## log_viral_gene.5 -0.0494551 0.0427692 -1.156 0.24816
## log_viral_gene.6 0.0005646 0.0428454 0.013 0.98949
## log_viral_gene.7 -0.0275667 0.0428398 -0.643 0.52024
## log_viral_gene.8 0.0607833 0.0428001 1.420 0.15625
## log_viral_gene.9 -0.0885477 0.0427327 -2.072 0.03882 *
## log_viral_gene.10 0.0100525 0.0425001 0.237 0.81313
## log_viral_gene.11 0.0635569 0.0425085 1.495 0.13558
## log_viral_gene.12 -0.0298949 0.0419159 -0.713 0.47609
## log_viral_gene.13 -0.0213158 0.0419694 -0.508 0.61178
## log_viral_gene.14 -0.0186732 0.0308532 -0.605 0.54533
## mean_precipation.t -0.0681444 0.0428634 -1.590 0.11258
## mean_temp.t 0.0012639 0.0014208 0.890 0.37417
## log_mean_new_cases.1 0.4409079 0.0470515 9.371 < 2e-16 ***
## log_mean_new_cases.2 0.1235043 0.0515498 2.396 0.01699 *
## log_mean_new_cases.3 0.0343170 0.0513172 0.669 0.50402
## log_mean_new_cases.4 0.1509435 0.0511587 2.950 0.00334 **
## log_mean_new_cases.5 0.0836452 0.0513815 1.628 0.10424
## log_mean_new_cases.6 0.0743482 0.0509181 1.460 0.14495
## log_mean_new_cases.7 0.1655124 0.0510728 3.241 0.00128 **
## log_mean_new_cases.8 -0.0494097 0.0515274 -0.959 0.33812
## log_mean_new_cases.9 -0.0722661 0.0471558 -1.532 0.12610
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3781 on 449 degrees of freedom
## Multiple R-squared: 0.9048, Adjusted R-squared: 0.8993
## F-statistic: 164.1 on 26 and 449 DF, p-value: < 2.2e-16
remove <- list(p =list(mean_precipation = c(1:14),
mean_temp= c(1:14)))
mod_ardl914_weather_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
mean_temp,data = full_cases_wastewater_weather_data_hanover_train,
p=14,q=9,
remove = remove)
summary(mod_ardl914_weather_hanover)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.44868 -0.20312 -0.00174 0.24075 1.06440
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4196023 0.2826546 -1.485 0.13838
## log_viral_gene.t 0.0899460 0.0306394 2.936 0.00350 **
## log_viral_gene.1 -0.0165224 0.0415725 -0.397 0.69123
## log_viral_gene.2 -0.0498911 0.0415549 -1.201 0.23054
## log_viral_gene.3 0.0439677 0.0423291 1.039 0.29950
## log_viral_gene.4 0.0578390 0.0424261 1.363 0.17347
## log_viral_gene.5 -0.0494551 0.0427692 -1.156 0.24816
## log_viral_gene.6 0.0005646 0.0428454 0.013 0.98949
## log_viral_gene.7 -0.0275667 0.0428398 -0.643 0.52024
## log_viral_gene.8 0.0607833 0.0428001 1.420 0.15625
## log_viral_gene.9 -0.0885477 0.0427327 -2.072 0.03882 *
## log_viral_gene.10 0.0100525 0.0425001 0.237 0.81313
## log_viral_gene.11 0.0635569 0.0425085 1.495 0.13558
## log_viral_gene.12 -0.0298949 0.0419159 -0.713 0.47609
## log_viral_gene.13 -0.0213158 0.0419694 -0.508 0.61178
## log_viral_gene.14 -0.0186732 0.0308532 -0.605 0.54533
## mean_precipation.t -0.0681444 0.0428634 -1.590 0.11258
## mean_temp.t 0.0012639 0.0014208 0.890 0.37417
## log_mean_new_cases.1 0.4409079 0.0470515 9.371 < 2e-16 ***
## log_mean_new_cases.2 0.1235043 0.0515498 2.396 0.01699 *
## log_mean_new_cases.3 0.0343170 0.0513172 0.669 0.50402
## log_mean_new_cases.4 0.1509435 0.0511587 2.950 0.00334 **
## log_mean_new_cases.5 0.0836452 0.0513815 1.628 0.10424
## log_mean_new_cases.6 0.0743482 0.0509181 1.460 0.14495
## log_mean_new_cases.7 0.1655124 0.0510728 3.241 0.00128 **
## log_mean_new_cases.8 -0.0494097 0.0515274 -0.959 0.33812
## log_mean_new_cases.9 -0.0722661 0.0471558 -1.532 0.12610
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3781 on 449 degrees of freedom
## Multiple R-squared: 0.9048, Adjusted R-squared: 0.8993
## F-statistic: 164.1 on 26 and 449 DF, p-value: < 2.2e-16
f_ardl914_weather_hanover <- forecast(mod_ardl914_weather_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,c(7,4,5)]),
h=14, interval = TRUE)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl914_weather_hanover$forecasts)
## [1] NA
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl914_weather_hanover$forecasts)
## [1] NA
checkresiduals(mod_ardl914_weather_hanover)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## 0.1448596577 -0.2701201876 -0.0360931405 -0.0023485448 0.0614578988
## 20 21 22 23 24
## 0.1902709444 0.2167612468 0.2534180814 0.0124906080 -0.0673391373
## 25 26 27 28 29
## -0.0572702390 -0.2956707576 0.6586152219 -0.1967724881 0.3798786680
## 30 31 32 33 34
## -0.4124229228 0.1839462314 -0.0076684908 -0.0769000060 0.2646881644
## 35 36 37 38 39
## 0.5610365432 0.2712477509 -0.1262058115 -0.1521341269 0.0523926079
## 40 41 42 43 44
## 0.0146428507 0.2019169199 -0.1244961774 -0.2311368899 0.1351136637
## 45 46 47 48 49
## -0.1218037800 -0.1837856990 -0.3071713989 0.0614630997 -0.4039120906
## 50 51 52 53 54
## 0.2462180252 -0.1617782398 -0.4308241779 0.2552498170 -0.1901251331
## 55 56 57 58 59
## 0.2568329735 0.4013289783 0.2721695003 0.0276153111 0.0247032832
## 60 61 62 63 64
## 0.1178572409 0.0793948964 0.2863596282 0.0604595987 -0.1192258153
## 65 66 67 68 69
## -0.2925498100 0.6541275645 0.2461047892 0.1015965807 -0.1803475905
## 70 71 72 73 74
## 0.3982735025 -0.0515859099 -0.0712090424 0.1070034088 -0.2364975135
## 75 76 77 78 79
## 0.0917511945 0.3081202359 0.2494557351 0.1238129916 -0.0219880744
## 80 81 82 83 84
## 0.3699282197 0.2198207279 0.0853133893 0.0101973100 -0.0981652886
## 85 86 87 88 89
## 0.2428157130 -0.1147516223 0.2060508846 -0.4271974859 -0.1076335006
## 90 91 92 93 94
## -0.2607917807 0.1505724942 -0.3336551074 -0.0960079920 -0.3299922517
## 95 96 97 98 99
## 0.2729659022 0.0323823250 -0.3264036153 0.1467719366 0.2038252861
## 100 101 102 103 104
## 0.1678817368 0.0567068150 0.0143095019 -0.0332827477 0.3534076498
## 105 106 107 108 109
## -0.2516006641 -1.1966543723 0.6407796182 -0.2063580231 0.2571231484
## 110 111 112 113 114
## -0.0332380415 0.3990948958 0.5476541393 -1.0538441885 0.7476816688
## 115 116 117 118 119
## 0.1201529499 0.0390908815 -0.0044770235 0.1391930242 -0.6692331598
## 120 121 122 123 124
## 0.2748240303 0.1093519383 -0.5776323059 -0.0311510605 -1.0608884452
## 125 126 127 128 129
## 0.4334959694 0.2732316818 -0.5354295434 0.5015650908 -0.1275566833
## 130 131 132 133 134
## 0.5014545010 -0.1436873305 0.1070813564 -0.5769546261 -0.2082160272
## 135 136 137 138 139
## 0.2809632949 -0.9246196166 -0.4340405494 0.6755398314 0.3328607260
## 140 141 142 143 144
## -0.3157896644 0.0061258138 -0.6882871567 0.8801283126 -0.7417254031
## 145 146 147 148 149
## 0.2313981319 -0.3587580249 0.1317677939 0.2569225816 -0.2974444378
## 150 151 152 153 154
## -0.2526086093 0.0204295192 -0.0377821688 0.0458331350 0.2584724319
## 155 156 157 158 159
## 0.1425418504 -0.3248379644 -0.0432838470 -0.1958435776 -0.0355487532
## 160 161 162 163 164
## 0.0033981643 0.4994066310 0.3561140463 -0.5568123929 0.0186486862
## 165 166 167 168 169
## -0.2286895116 -0.0056299829 0.0449214538 0.2374491703 0.2088266533
## 170 171 172 173 174
## -0.2500962338 -0.0716556393 -0.0368066937 -0.0903040122 -0.2338913764
## 175 176 177 178 179
## 0.7281559925 -0.0986996855 -0.4739481563 -0.3494835798 -0.4689635479
## 180 181 182 183 184
## 0.4176889498 -0.2120496643 -0.0484133742 0.2232366132 -0.3127062640
## 185 186 187 188 189
## 0.5201793630 -0.0541719126 -0.4684923147 -0.2943154516 0.0311312426
## 190 191 192 193 194
## 0.7069826820 -0.5017134651 -0.6043477636 1.0644039499 0.0676783365
## 195 196 197 198 199
## 0.5785212979 -0.4417657714 -0.6833519080 -0.7905143085 0.5643392885
## 200 201 202 203 204
## 0.0608334090 0.7324729182 0.3843340185 0.7305501506 0.8376321903
## 205 206 207 208 209
## 0.1675239318 0.0003303264 -0.2505294583 0.0558129761 -0.0566150012
## 210 211 212 213 214
## -0.0788039326 0.2518297493 0.0976738023 0.2603057210 -0.0747493020
## 215 216 217 218 219
## -0.0105319785 0.4133681646 0.0315770921 0.0036905159 0.0403785431
## 220 221 222 223 224
## 0.1059570929 -0.1024301168 -0.1827900433 0.0808330295 -0.1861427869
## 225 226 227 228 229
## 0.2023718001 0.1818968531 -0.0489599644 0.0123491378 0.3219833096
## 230 231 232 233 234
## 0.0316534704 -0.2581167043 0.0583085955 0.5700003627 0.5954262952
## 235 236 237 238 239
## 0.2848515688 0.3462760650 -0.2143090413 -0.5621602103 -0.2730037821
## 240 241 242 243 244
## -0.1714468414 0.0391053959 0.2178093368 -0.0687005226 -0.2351469411
## 245 246 247 248 249
## -0.1119914021 -0.2920024378 -0.8190123539 0.3833744432 0.0343693485
## 250 251 252 253 254
## -0.1799182471 0.1419980348 -0.2378685784 0.0612286255 0.4011171061
## 255 256 257 258 259
## -0.2375622209 -0.2020381030 -0.1467294753 0.0970864036 -0.1303181727
## 260 261 262 263 264
## -0.2922809287 -0.1274206410 0.0614984843 0.0306651595 -0.0315891801
## 265 266 267 268 269
## -0.4377999185 -0.0640159645 -0.0665969726 -0.1057555472 -0.1456231253
## 270 271 272 273 274
## -0.2403413712 -0.4356968988 0.2371785611 -0.1979393623 -0.7242058997
## 275 276 277 278 279
## 0.3631037673 0.0660423780 -0.3932058015 0.3381009698 -0.1578318148
## 280 281 282 283 284
## 0.2446530443 -0.2490493023 -0.0060098678 -0.1666019392 -0.0147796306
## 285 286 287 288 289
## 0.1491540493 0.1799059449 -0.2701860074 -0.3336560591 -0.0011273664
## 290 291 292 293 294
## 0.1122159231 -1.4486775860 -0.7554797047 -0.5746964907 0.7330382116
## 295 296 297 298 299
## -0.3739401710 -0.0293626674 -0.1062926070 0.4555527460 -0.6191352352
## 300 301 302 303 304
## 0.2515544686 -0.4484179583 -0.0539196850 -0.0703001396 0.4412054622
## 305 306 307 308 309
## -0.0824357825 -0.6025586483 -0.0306639131 0.3063996659 0.0700235724
## 310 311 312 313 314
## 0.6314927406 -0.4080936508 -0.1927422244 0.1990798734 0.6016683886
## 315 316 317 318 319
## 0.8019766719 -0.3451904574 0.2021213138 0.3879885659 0.3250598275
## 320 321 322 323 324
## 0.0189059253 -0.5709861923 -0.1164553442 0.5403781221 -0.2627692245
## 325 326 327 328 329
## -0.3169081826 -0.1253828791 -1.2784265672 -0.0530309577 0.6622065640
## 330 331 332 333 334
## 0.8513889793 0.5071828163 0.2751323869 -0.1056722935 0.2597791745
## 335 336 337 338 339
## -0.1235285176 -0.2939064408 0.2065963386 -0.0239880120 -0.2163514465
## 340 341 342 343 344
## 0.5265352521 0.2442196920 -0.8069743153 0.5303510545 0.3661638068
## 345 346 347 348 349
## 0.1456767410 0.2254324794 -0.0622707640 0.2238190550 0.3614328646
## 350 351 352 353 354
## 0.2400658850 0.3625992808 0.4559347604 -0.1228078173 0.5488429791
## 355 356 357 358 359
## 0.3378106674 -0.5142521325 -0.6996584252 0.5752441605 0.8005401107
## 360 361 362 363 364
## 0.6971581088 0.5404816367 0.5959684820 -0.1407414080 -0.2717051872
## 365 366 367 368 369
## 0.1494480049 0.3511771343 0.2917885557 0.0074824259 0.4390593537
## 370 371 372 373 374
## 0.3058360246 -0.0935495226 -0.1221744215 0.1195427603 0.0330591162
## 375 376 377 378 379
## 0.0835421921 0.1953184256 0.2587582992 -0.1727205133 -0.2014964087
## 380 381 382 383 384
## 0.2696099072 0.4303745555 0.2957669048 0.0586658145 -0.8343168476
## 385 386 387 388 389
## -0.6320853484 0.1052786463 0.3578813808 -0.1597636232 -0.0698243549
## 390 391 392 393 394
## 0.0748995031 0.0953170765 -0.3862987160 -0.2631336781 0.0133731403
## 395 396 397 398 399
## -0.1520176959 -0.0329479126 -0.2016032852 -0.1198533160 -0.4029360466
## 400 401 402 403 404
## -0.1847271364 -0.0641867390 -0.0128305703 -0.2279985145 -0.0084782650
## 405 406 407 408 409
## -0.0462475260 -0.7000125738 0.0372211934 -0.2341463727 -0.3780974398
## 410 411 412 413 414
## -0.0496353806 -0.2560522954 -0.0968365285 -0.4384285480 0.3604897184
## 415 416 417 418 419
## -0.0987845652 -0.1786535235 0.0591103709 -0.0073719556 -0.4323526677
## 420 421 422 423 424
## -0.5870019956 -0.3829624629 -0.0854455708 -0.8061198733 -0.4404499533
## 425 426 427 428 429
## 0.4968442278 -0.3541596113 0.3906029074 0.2237221664 0.2306070112
## 430 431 432 433 434
## -0.4696798907 0.2617004917 0.1605134521 -0.3456480710 0.3304342073
## 435 436 437 438 439
## 0.0332609729 -0.5598183560 0.0368764989 -0.1381071890 -0.0564951439
## 440 441 442 443 444
## 0.1711902095 0.5702508467 0.8419144507 -0.5441600274 -0.0916706866
## 445 446 447 448 449
## -0.0946295813 -0.0946213847 0.0025350902 0.1844767897 0.0461788716
## 450 451 452 453 454
## -0.3785542075 -0.0668567860 -0.4171291593 -0.0466616887 -0.0843935574
## 455 456 457 458 459
## 0.0799719288 -0.0275224466 0.0429623434 -0.2524154955 0.1403735191
## 460 461 462 463 464
## 0.7391715299 -0.6646226729 -0.1359374782 -0.1279936971 -0.0095669157
## 465 466 467 468 469
## 0.4938193634 0.6910727667 -0.1878455476 -0.1797075425 -0.5611030102
## 470 471 472 473 474
## -0.4920585261 0.2236945721 0.1492238259 -0.4326876463 -0.2258603616
## 475 476 477 478 479
## -0.5967218108 1.0479218427 -0.7550557877 0.2755654743 0.3655854654
## 480 481 482 483 484
## 0.3705433546 0.3725452304 0.6099959922 -0.8424478517 -0.0910911059
## 485 486 487 488 489
## 0.2331111264 0.0330803861 0.1782664091 -0.1275199172 0.3380705753
## 490
## 0.0008309683
exp(f_ardl914_weather_hanover$forecasts[1,2])
## [1] 1.44021
exp(f_ardl914_weather_hanover$forecasts[1,1])
## [1] 0.6995792
exp(f_ardl914_weather_hanover$forecasts[1,3])
## [1] 3.045355
exp(f_ardl914_weather_hanover$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_hanover_test[1,6])
## [1] 0.332002
exp(f_ardl914_weather_hanover$forecasts[7,2])
## [1] 1.868935
exp(f_ardl914_weather_hanover$forecasts[7,1])
## [1] 0.7130021
exp(f_ardl914_weather_hanover$forecasts[7,3])
## [1] 4.942952
exp(f_ardl914_weather_hanover$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_hanover_test[7,6])
## [1] -0.389472
exp(f_ardl914_weather_hanover$forecasts[14,2])
## [1] 2.388859
exp(f_ardl914_weather_hanover$forecasts[14,1])
## [1] 0.7341548
exp(f_ardl914_weather_hanover$forecasts[14,3])
## [1] 6.731812
exp(f_ardl914_weather_hanover$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_hanover_test[14,6])
## [1] 1.549632
remove <- list(p =list(mean_precipation = c(1:14),
mean_temp= c(1:14)))
mod_ardl1414_weather_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
mean_temp,data = full_cases_wastewater_weather_data_hanover_train,
p=14,q=14,
remove = remove)
summary(mod_ardl1414_weather_hanover)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.43294 -0.19875 0.00512 0.22626 1.08988
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4670952 0.2786445 -1.676 0.094381 .
## log_viral_gene.t 0.0922004 0.0301820 3.055 0.002388 **
## log_viral_gene.1 -0.0154866 0.0409748 -0.378 0.705645
## log_viral_gene.2 -0.0526942 0.0409847 -1.286 0.199216
## log_viral_gene.3 0.0409139 0.0417076 0.981 0.327141
## log_viral_gene.4 0.0504114 0.0418060 1.206 0.228521
## log_viral_gene.5 -0.0560534 0.0421717 -1.329 0.184474
## log_viral_gene.6 0.0043584 0.0423183 0.103 0.918017
## log_viral_gene.7 -0.0216016 0.0423224 -0.510 0.610021
## log_viral_gene.8 0.0553156 0.0422959 1.308 0.191610
## log_viral_gene.9 -0.0876445 0.0423616 -2.069 0.039128 *
## log_viral_gene.10 0.0087567 0.0420620 0.208 0.835179
## log_viral_gene.11 0.0611382 0.0420571 1.454 0.146737
## log_viral_gene.12 -0.0231088 0.0414371 -0.558 0.577341
## log_viral_gene.13 -0.0195318 0.0414581 -0.471 0.637785
## log_viral_gene.14 -0.0070912 0.0309912 -0.229 0.819120
## mean_precipation.t -0.0692615 0.0422459 -1.639 0.101820
## mean_temp.t 0.0009596 0.0014032 0.684 0.494412
## log_mean_new_cases.1 0.4162182 0.0473614 8.788 < 2e-16 ***
## log_mean_new_cases.2 0.1252954 0.0514266 2.436 0.015227 *
## log_mean_new_cases.3 0.0254412 0.0512488 0.496 0.619840
## log_mean_new_cases.4 0.1660338 0.0511644 3.245 0.001263 **
## log_mean_new_cases.5 0.1277823 0.0516267 2.475 0.013691 *
## log_mean_new_cases.6 0.1024951 0.0516406 1.985 0.047784 *
## log_mean_new_cases.7 0.1919035 0.0520010 3.690 0.000252 ***
## log_mean_new_cases.8 -0.0193370 0.0521377 -0.371 0.710901
## log_mean_new_cases.9 -0.0453096 0.0521161 -0.869 0.385100
## log_mean_new_cases.10 0.0385100 0.0517716 0.744 0.457364
## log_mean_new_cases.11 -0.0711252 0.0510386 -1.394 0.164148
## log_mean_new_cases.12 -0.1561833 0.0510005 -3.062 0.002329 **
## log_mean_new_cases.13 -0.0166371 0.0511387 -0.325 0.745082
## log_mean_new_cases.14 0.0536765 0.0470368 1.141 0.254419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3718 on 444 degrees of freedom
## Multiple R-squared: 0.9089, Adjusted R-squared: 0.9026
## F-statistic: 143 on 31 and 444 DF, p-value: < 2.2e-16
f_ardl1414_weather_hanover <- forecast(mod_ardl1414_weather_hanover, x= t(full_cases_wastewater_weather_data_hanover_test[,c(7,4,5)]),h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl1414_weather_hanover$forecasts)
## [1] 0.3589144
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl1414_weather_hanover$forecasts)
## [1] 0.2502069
checkresiduals(mod_ardl1414_weather_hanover)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## 2.270589e-01 -2.410311e-01 -2.854062e-02 3.283958e-02 1.116750e-01
## 20 21 22 23 24
## 2.098113e-01 1.770425e-01 2.020030e-01 3.031835e-02 -1.507969e-02
## 25 26 27 28 29
## -2.307308e-02 -2.599690e-01 6.483056e-01 -2.533463e-01 3.131980e-01
## 30 31 32 33 34
## -4.168900e-01 1.862153e-01 7.073310e-03 -4.502889e-02 2.929331e-01
## 35 36 37 38 39
## 5.636111e-01 2.533170e-01 -1.554401e-01 -1.270906e-01 1.335652e-01
## 40 41 42 43 44
## 5.100574e-02 1.784663e-01 -1.903397e-01 -2.833543e-01 1.071710e-01
## 45 46 47 48 49
## -1.301165e-01 -1.215357e-01 -2.010920e-01 1.194348e-01 -4.364003e-01
## 50 51 52 53 54
## 1.897035e-01 -1.253740e-01 -3.377345e-01 3.549827e-01 -1.616130e-01
## 55 56 57 58 59
## 2.351323e-01 4.593852e-01 3.486261e-01 5.279231e-02 4.598862e-02
## 60 61 62 63 64
## 1.266101e-01 6.564988e-02 2.885187e-01 2.034467e-02 -2.128808e-01
## 65 66 67 68 69
## -3.537216e-01 5.710413e-01 2.231440e-01 1.515378e-01 -1.246995e-01
## 70 71 72 73 74
## 4.039996e-01 -6.561615e-02 -7.021196e-02 1.486042e-01 -1.800846e-01
## 75 76 77 78 79
## 1.241210e-01 2.429562e-01 1.853579e-01 1.956630e-01 1.019016e-01
## 80 81 82 83 84
## 3.981707e-01 2.168091e-01 9.741278e-02 -1.624088e-02 -1.804782e-01
## 85 86 87 88 89
## 1.605165e-01 -1.924623e-01 1.704031e-01 -3.871244e-01 -1.060204e-01
## 90 91 92 93 94
## -3.125177e-01 1.028900e-01 -2.931317e-01 1.200058e-02 -2.323099e-01
## 95 96 97 98 99
## 3.132134e-01 6.486246e-02 -2.600250e-01 2.228510e-01 2.649795e-01
## 100 101 102 103 104
## 1.780704e-01 5.836262e-02 4.590045e-02 -3.047084e-02 3.266498e-01
## 105 106 107 108 109
## -2.911229e-01 -1.230005e+00 6.487112e-01 -2.004594e-01 1.605844e-01
## 110 111 112 113 114
## -4.134065e-02 4.741153e-01 6.270153e-01 -9.873207e-01 7.694942e-01
## 115 116 117 118 119
## 2.102079e-01 1.083709e-01 -9.440471e-02 -9.885186e-03 -6.749762e-01
## 120 121 122 123 124
## 2.938716e-01 1.033343e-01 -5.714445e-01 5.203362e-02 -1.047539e+00
## 125 126 127 128 129
## 2.643079e-01 3.037395e-01 -4.143345e-01 5.311315e-01 -4.646205e-02
## 130 131 132 133 134
## 5.165328e-01 -1.668338e-01 1.749692e-01 -4.424815e-01 -1.605759e-01
## 135 136 137 138 139
## 1.982563e-01 -1.051565e+00 -4.278540e-01 7.661721e-01 3.480531e-01
## 140 141 142 143 144
## -2.606894e-01 1.146758e-01 -5.939083e-01 9.089404e-01 -7.126457e-01
## 145 146 147 148 149
## 1.843867e-01 -3.274030e-01 1.535327e-01 9.671142e-02 -4.177192e-01
## 150 151 152 153 154
## -1.492836e-01 1.424027e-01 -4.550772e-02 -6.086472e-02 2.530463e-01
## 155 156 157 158 159
## 2.403866e-01 -2.852644e-01 -8.697092e-03 -1.486754e-01 2.136880e-02
## 160 161 162 163 164
## 5.256361e-02 4.410108e-01 3.082210e-01 -5.653917e-01 -1.594318e-02
## 165 166 167 168 169
## -2.104119e-01 4.846740e-02 6.595354e-02 1.794267e-01 1.425456e-01
## 170 171 172 173 174
## -2.851416e-01 -1.072190e-01 -2.198649e-02 3.733810e-03 -1.903774e-01
## 175 176 177 178 179
## 6.596738e-01 -1.422580e-01 -5.072102e-01 -3.332111e-01 -4.047743e-01
## 180 181 182 183 184
## 4.981373e-01 -1.613849e-01 -8.710442e-02 1.975234e-01 -3.284858e-01
## 185 186 187 188 189
## 4.366427e-01 -2.929455e-02 -3.150026e-01 -2.887443e-01 -1.110311e-01
## 190 191 192 193 194
## 5.828399e-01 -5.054694e-01 -5.554057e-01 1.089883e+00 1.079370e-01
## 195 196 197 198 199
## 5.845387e-01 -4.269165e-01 -6.024582e-01 -7.885443e-01 3.826554e-01
## 200 201 202 203 204
## -1.090543e-01 7.362514e-01 5.068109e-01 6.526271e-01 7.404637e-01
## 205 206 207 208 209
## 2.876024e-01 1.235561e-01 -2.003769e-01 -4.335005e-02 -3.909530e-01
## 210 211 212 213 214
## -4.063492e-01 1.302842e-01 9.992110e-02 2.433238e-01 -9.023134e-02
## 215 216 217 218 219
## 1.816177e-02 4.684848e-01 3.205087e-02 -3.001481e-02 2.641413e-02
## 220 221 222 223 224
## 9.420464e-02 -1.302035e-01 -1.937320e-01 1.056923e-01 -1.769417e-01
## 225 226 227 228 229
## 1.650905e-01 1.371480e-01 -6.742795e-02 4.294468e-02 3.394963e-01
## 230 231 232 233 234
## 3.623700e-02 -2.380512e-01 8.886582e-02 5.534564e-01 5.494565e-01
## 235 236 237 238 239
## 2.701031e-01 3.499940e-01 -1.823197e-01 -5.764624e-01 -3.665840e-01
## 240 241 242 243 244
## -2.399389e-01 5.800127e-03 1.456074e-01 -1.744113e-01 -2.503231e-01
## 245 246 247 248 249
## -2.593299e-02 -2.109245e-01 -7.470054e-01 5.016789e-01 8.247269e-02
## 250 251 252 253 254
## -2.334856e-01 1.352606e-01 -1.413422e-01 1.489468e-01 4.864447e-01
## 255 256 257 258 259
## -1.285546e-01 -1.525437e-01 -1.349363e-01 -2.197406e-02 -2.305820e-01
## 260 261 262 263 264
## -2.144332e-01 -4.825002e-02 5.905773e-02 -9.467473e-05 -1.012822e-01
## 265 266 267 268 269
## -4.390793e-01 1.339791e-02 1.486407e-02 -6.623097e-02 -8.698252e-02
## 270 271 272 273 274
## -1.469226e-01 -3.847692e-01 2.592446e-01 -1.563856e-01 -7.027729e-01
## 275 276 277 278 279
## 3.872251e-01 1.088777e-01 -4.009366e-01 3.579363e-01 -8.794474e-02
## 280 281 282 283 284
## 2.805808e-01 -2.259005e-01 -4.829114e-02 -2.084944e-01 4.464939e-03
## 285 286 287 288 289
## 9.735779e-02 8.071994e-02 -2.421299e-01 -2.978718e-01 -3.637500e-02
## 290 291 292 293 294
## 1.016082e-01 -1.432937e+00 -7.801099e-01 -5.988665e-01 6.835698e-01
## 295 296 297 298 299
## -3.784937e-01 2.075589e-02 6.443711e-02 6.203824e-01 -5.498804e-01
## 300 301 302 303 304
## 2.926634e-01 -2.797025e-01 -1.389714e-03 -2.571800e-01 2.357038e-01
## 305 306 307 308 309
## -7.824636e-02 -4.796626e-01 -7.408385e-03 2.526975e-01 6.102977e-02
## 310 311 312 313 314
## 5.945919e-01 -4.786287e-01 -2.606658e-01 1.495578e-01 5.099051e-01
## 315 316 317 318 319
## 7.727305e-01 -2.495181e-01 2.124409e-01 2.689888e-01 2.482887e-01
## 320 321 322 323 324
## 1.687323e-02 -4.801578e-01 -6.831247e-02 4.085476e-01 -4.708001e-01
## 325 326 327 328 329
## -3.869036e-01 -3.669694e-03 -1.196805e+00 -1.982067e-01 5.794727e-01
## 330 331 332 333 334
## 8.667989e-01 5.591952e-01 3.124949e-01 -1.175088e-01 3.100643e-01
## 335 336 337 338 339
## -5.628794e-02 -3.417530e-01 1.429134e-01 -1.715225e-01 -5.417116e-01
## 340 341 342 343 344
## 3.233918e-01 3.238345e-01 -6.850812e-01 5.301461e-01 2.922436e-01
## 345 346 347 348 349
## 5.868424e-02 2.295316e-01 -2.265279e-02 2.586583e-01 4.498998e-01
## 350 351 352 353 354
## 2.433672e-01 2.754289e-01 4.642949e-01 -7.955589e-02 4.480241e-01
## 355 356 357 358 359
## 3.129450e-01 -5.415047e-01 -7.575037e-01 4.801098e-01 6.654430e-01
## 360 361 362 363 364
## 6.247283e-01 5.671282e-01 6.244267e-01 -1.339416e-01 -3.051507e-01
## 365 366 367 368 369
## 1.210243e-01 3.805827e-01 2.607641e-01 -2.324668e-01 1.644349e-01
## 370 371 372 373 374
## 2.601512e-01 1.885763e-02 -2.036669e-02 1.984214e-01 3.783876e-02
## 375 376 377 378 379
## -5.591532e-02 2.700763e-02 2.289714e-01 -8.509009e-02 -1.478307e-01
## 380 381 382 383 384
## 2.632013e-01 4.429521e-01 3.046121e-01 2.456644e-02 -8.530184e-01
## 385 386 387 388 389
## -6.399881e-01 8.274446e-02 3.372660e-01 -1.147495e-01 5.777909e-03
## 390 391 392 393 394
## 8.115420e-02 8.168821e-02 -2.934271e-01 -9.596380e-02 1.711521e-01
## 395 396 397 398 399
## -1.072358e-01 -1.756149e-01 -3.297276e-01 -7.229281e-02 -2.626040e-01
## 400 401 402 403 404
## -1.192008e-01 -3.874016e-02 4.834980e-02 -1.894929e-01 -2.641341e-02
## 405 406 407 408 409
## 2.998860e-03 -5.923718e-01 1.076647e-01 -1.770867e-01 -3.368716e-01
## 410 411 412 413 414
## -4.730343e-02 -2.775679e-01 -9.258815e-02 -3.649260e-01 4.165542e-01
## 415 416 417 418 419
## -3.994843e-02 -8.101042e-02 1.160832e-01 -1.315062e-02 -3.784094e-01
## 420 421 422 423 424
## -5.435940e-01 -4.024176e-01 -1.008230e-01 -7.923297e-01 -4.822691e-01
## 425 426 427 428 429
## 4.688669e-01 -2.561113e-01 4.838682e-01 3.077308e-01 3.607276e-01
## 430 431 432 433 434
## -3.344516e-01 2.781521e-01 9.937074e-02 -3.407697e-01 3.262542e-01
## 435 436 437 438 439
## -8.516648e-02 -6.544093e-01 3.181274e-02 -1.888867e-01 -1.122246e-01
## 440 441 442 443 444
## 2.259891e-01 5.806447e-01 7.792650e-01 -5.021219e-01 -6.116585e-02
## 445 446 447 448 449
## -1.312755e-01 -9.811521e-02 6.198102e-03 1.064235e-01 -2.131154e-02
## 450 451 452 453 454
## -4.170138e-01 -1.298564e-01 -4.328606e-01 6.861778e-02 6.498668e-02
## 455 456 457 458 459
## 5.746764e-02 -8.337697e-02 4.740934e-02 -2.839263e-01 1.589511e-01
## 460 461 462 463 464
## 8.343013e-01 -5.840918e-01 -1.865652e-01 -1.794954e-01 -7.253902e-02
## 465 466 467 468 469
## 3.748417e-01 6.494985e-01 -1.502770e-01 -1.396160e-01 -5.996783e-01
## 470 471 472 473 474
## -6.067145e-01 2.147969e-01 1.570543e-01 -5.606905e-01 -3.457215e-01
## 475 476 477 478 479
## -6.300701e-01 1.015372e+00 -6.281327e-01 4.363419e-01 4.222513e-01
## 480 481 482 483 484
## 3.018794e-01 2.582891e-01 5.830708e-01 -7.478106e-01 -4.883500e-02
## 485 486 487 488 489
## 1.577766e-01 -1.902995e-01 2.702728e-02 -1.168220e-01 2.425754e-01
## 490
## -9.335678e-02
remove <- list(p =list(mean_precipation = c(1:11),
mean_temp= c(1:11)))
mod_ardl1311_weather_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
mean_temp,data = full_cases_wastewater_weather_data_hanover_train,
p=11,q=13,
remove = remove)
summary(mod_ardl1311_weather_hanover)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.48048 -0.20447 -0.00048 0.21990 1.07006
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5562310 0.2710179 -2.052 0.040712 *
## log_viral_gene.t 0.0903774 0.0301453 2.998 0.002868 **
## log_viral_gene.1 -0.0175650 0.0409407 -0.429 0.668104
## log_viral_gene.2 -0.0497835 0.0408754 -1.218 0.223889
## log_viral_gene.3 0.0390321 0.0416497 0.937 0.349185
## log_viral_gene.4 0.0430543 0.0416091 1.035 0.301351
## log_viral_gene.5 -0.0527710 0.0418437 -1.261 0.207911
## log_viral_gene.6 0.0083179 0.0420137 0.198 0.843151
## log_viral_gene.7 -0.0302828 0.0417319 -0.726 0.468431
## log_viral_gene.8 0.0487226 0.0418839 1.163 0.245334
## log_viral_gene.9 -0.0754796 0.0411709 -1.833 0.067416 .
## log_viral_gene.10 0.0118713 0.0412826 0.288 0.773815
## log_viral_gene.11 0.0213976 0.0308429 0.694 0.488191
## mean_precipation.t -0.0708030 0.0421641 -1.679 0.093804 .
## mean_temp.t 0.0008344 0.0013988 0.597 0.551132
## log_mean_new_cases.1 0.4170950 0.0471616 8.844 < 2e-16 ***
## log_mean_new_cases.2 0.1142583 0.0507139 2.253 0.024741 *
## log_mean_new_cases.3 0.0273515 0.0507571 0.539 0.590243
## log_mean_new_cases.4 0.1693411 0.0507479 3.337 0.000918 ***
## log_mean_new_cases.5 0.1279650 0.0511656 2.501 0.012740 *
## log_mean_new_cases.6 0.1062070 0.0514707 2.063 0.039644 *
## log_mean_new_cases.7 0.2079812 0.0510988 4.070 5.55e-05 ***
## log_mean_new_cases.8 -0.0153943 0.0518576 -0.297 0.766713
## log_mean_new_cases.9 -0.0446710 0.0515833 -0.866 0.386953
## log_mean_new_cases.10 0.0447135 0.0509052 0.878 0.380214
## log_mean_new_cases.11 -0.0701170 0.0508681 -1.378 0.168763
## log_mean_new_cases.12 -0.1571059 0.0502739 -3.125 0.001893 **
## log_mean_new_cases.13 0.0009672 0.0463921 0.021 0.983375
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3717 on 449 degrees of freedom
## Multiple R-squared: 0.9082, Adjusted R-squared: 0.9027
## F-statistic: 164.5 on 27 and 449 DF, p-value: < 2.2e-16
f_ardl1311_weather_hanover <- forecast(mod_ardl1311_weather_hanover, x= t(full_cases_wastewater_weather_data_hanover_test[,c(7,4,5)]),h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl1311_weather_hanover$forecasts)
## [1] 0.379521
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl1311_weather_hanover$forecasts)
## [1] 0.2620331
checkresiduals(mod_ardl1311_weather_hanover)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18
## 0.2792092891 0.2223521723 -0.2190584141 -0.0004582325 0.0430956794
## 19 20 21 22 23
## 0.1140686676 0.2188521455 0.1827547011 0.2120835765 0.0387689363
## 24 25 26 27 28
## -0.0153983268 -0.0263591102 -0.2528857831 0.6479000707 -0.2573923315
## 29 30 31 32 33
## 0.3278707544 -0.4335560505 0.1767482429 -0.0093173522 -0.0427566444
## 34 35 36 37 38
## 0.2964485394 0.5520989204 0.2610007803 -0.1411617878 -0.1548387575
## 39 40 41 42 43
## 0.1129916496 0.0359343309 0.2235930161 -0.2176759337 -0.2630381821
## 44 45 46 47 48
## 0.1217436895 -0.1125062458 -0.1221446751 -0.2050573223 0.1152355625
## 49 50 51 52 53
## -0.4334428939 0.2191539651 -0.0985142772 -0.3269122377 0.3652177348
## 54 55 56 57 58
## -0.1591276786 0.2529923775 0.4645336683 0.3418526100 0.0651660934
## 59 60 61 62 63
## 0.0498894181 0.1333549535 0.0539981440 0.2568127925 -0.0301109652
## 64 65 66 67 68
## -0.2159717327 -0.3619569831 0.5444880064 0.2197994363 0.1223855205
## 69 70 71 72 73
## -0.1433320385 0.4050011094 -0.0472916020 -0.1244829019 0.1212334265
## 74 75 76 77 78
## -0.1643920577 0.1649665715 0.3148983662 0.2188739493 0.2196154719
## 79 80 81 82 83
## 0.1637177077 0.4556781518 0.2328557803 0.1176943491 -0.0523253956
## 84 85 86 87 88
## -0.1852388035 0.1561792310 -0.2044685620 0.1575807491 -0.4089961927
## 89 90 91 92 93
## -0.1075103202 -0.3493042662 0.0875308187 -0.2827491268 0.0681498800
## 94 95 96 97 98
## -0.1838917201 0.3496427178 0.1031812207 -0.2170489164 0.2321295201
## 99 100 101 102 103
## 0.2881512421 0.2432880124 0.1087994681 0.0423976575 -0.0275973948
## 104 105 106 107 108
## 0.2754592693 -0.3084067285 -1.2425451529 0.6536287786 -0.2254422586
## 109 110 111 112 113
## 0.1778788970 -0.0311995188 0.4617557753 0.6247184530 -0.9637168430
## 114 115 116 117 118
## 0.7915959699 0.2065183849 0.1334692730 -0.0812679060 -0.0044308145
## 119 120 121 122 123
## -0.6729066125 0.2527654281 0.1258199114 -0.5781291148 0.0780429480
## 124 125 126 127 128
## -1.0596241181 0.2624293994 0.3399975854 -0.4742550033 0.5573667182
## 129 130 131 132 133
## -0.0273250388 0.5439192488 -0.1640590307 0.1986528499 -0.4634757317
## 134 135 136 137 138
## -0.1409074048 0.1513350259 -1.0702373820 -0.3815010115 0.7385526952
## 139 140 141 142 143
## 0.4135186508 -0.1933050517 0.1186540230 -0.5319396209 0.9428281227
## 144 145 146 147 148
## -0.6743453499 0.1741235692 -0.3282807192 0.1465632601 0.0768463947
## 149 150 151 152 153
## -0.4370417551 -0.1878569571 0.1104968155 -0.0331266216 -0.0009659063
## 154 155 156 157 158
## 0.2642048740 0.2551870499 -0.3571152050 0.0364773733 -0.1678424579
## 159 160 161 162 163
## 0.0760519218 0.0734234748 0.4515469937 0.3324520916 -0.5003708848
## 164 165 166 167 168
## 0.0121905585 -0.2206893272 0.0309751377 0.0015485862 0.1560330127
## 169 170 171 172 173
## 0.1538470293 -0.2965923405 -0.0893191802 -0.0256117117 -0.0049357069
## 174 175 176 177 178
## -0.1451797589 0.7007605318 -0.1171548158 -0.5609838151 -0.3297330474
## 179 180 181 182 183
## -0.4007532747 0.5156145861 -0.1281270089 -0.0396250894 0.2306807458
## 184 185 186 187 188
## -0.3314126297 0.5311022130 0.0110412678 -0.3205536303 -0.3435568100
## 189 190 191 192 193
## -0.0967063380 0.5897078940 -0.5231677113 -0.6631972973 1.0295561009
## 194 195 196 197 198
## 0.1410488299 0.6216952250 -0.2980279294 -0.5352757961 -0.8046455397
## 199 200 201 202 203
## 0.4587783584 -0.1101950535 0.7026397219 0.4671648088 0.5864009355
## 204 205 206 207 208
## 0.7635009441 0.2941954226 0.0911131940 -0.1545182065 -0.0589582640
## 209 210 211 212 213
## -0.3848578923 -0.3887562572 0.1037023776 -0.0007341046 0.1962100291
## 214 215 216 217 218
## -0.1362748238 0.0152615013 0.4562544469 0.0528927392 -0.0050196194
## 219 220 221 222 223
## 0.0210566755 0.1077685964 -0.1239874781 -0.1912011574 0.0926152831
## 224 225 226 227 228
## -0.1608177914 0.1864151940 0.1286578794 -0.0860102561 0.0332059193
## 229 230 231 232 233
## 0.3231851093 0.0447942339 -0.2175589438 0.0973174382 0.5409912839
## 234 235 236 237 238
## 0.5362323934 0.2717514349 0.3330050536 -0.1876589389 -0.5636820375
## 239 240 241 242 243
## -0.3631886405 -0.2533945272 -0.0599367454 0.0801870131 -0.1930634304
## 244 245 246 247 248
## -0.2437629297 -0.0838669835 -0.2578363609 -0.7281421946 0.6096452143
## 249 250 251 252 253
## 0.1037700984 -0.2031903407 0.1696213925 -0.2343407797 0.1056715136
## 254 255 256 257 258
## 0.5031965342 -0.0242289360 -0.0920323452 -0.1053154291 -0.0284473025
## 259 260 261 262 263
## -0.2529086317 -0.2256351353 -0.1077326645 0.0405093192 -0.0100015579
## 264 265 266 267 268
## -0.1052045355 -0.4380843364 0.0012626149 0.0055020522 -0.0485837388
## 269 270 271 272 273
## -0.0960285994 -0.1432887442 -0.3775066192 0.2956738806 -0.1331706519
## 274 275 276 277 278
## -0.6906226520 0.3986158619 0.1412935657 -0.3827672845 0.3736767105
## 279 280 281 282 283
## -0.1110182417 0.2574668738 -0.2291004891 -0.0544480392 -0.2394291686
## 284 285 286 287 288
## -0.0068378073 0.0639766300 0.0693648943 -0.2512992996 -0.3400284807
## 289 290 291 292 293
## -0.0443239024 0.0501794032 -1.4804806186 -0.7742674801 -0.6205856905
## 294 295 296 297 298
## 0.6951801328 -0.3911061912 0.0334865252 0.0638419292 0.6343555456
## 299 300 301 302 303
## -0.5252855911 0.3356927781 -0.2913467654 -0.0057207774 -0.2456774103
## 304 305 306 307 308
## 0.2844134468 -0.1202075309 -0.5039219938 -0.0630668271 0.2525002406
## 309 310 311 312 313
## 0.0329964992 0.5758349287 -0.5318091034 -0.2669606511 0.0971245955
## 314 315 316 317 318
## 0.4754378591 0.6900214099 -0.2781963391 0.1856142504 0.1733359866
## 319 320 321 322 323
## 0.2199022717 -0.0004822604 -0.4634399895 -0.0255919113 0.4190566054
## 324 325 326 327 328
## -0.4300051624 -0.2922234057 0.0205397200 -1.2338653080 -0.1987533541
## 329 330 331 332 333
## 0.6060958218 0.8299209435 0.5499253179 0.3417917055 -0.1058034160
## 334 335 336 337 338
## 0.3285676144 -0.0779490281 -0.3749522976 0.1370796909 -0.1989325265
## 339 340 341 342 343
## -0.5708555106 0.3087925196 0.2354777976 -0.7472563495 0.4961084959
## 344 345 346 347 348
## 0.2745584850 0.0646891804 0.2418352201 -0.0816197099 0.2474334602
## 349 350 351 352 353
## 0.4907970235 0.1433239645 0.2343814142 0.4897963124 0.0919229323
## 354 355 356 357 358
## 0.5459981099 0.3396803715 -0.5918853621 -0.7659527793 0.4577546744
## 359 360 361 362 363
## 0.6248086019 0.6187538548 0.5305476239 0.6106716818 -0.1302924559
## 364 365 366 367 368
## -0.2752522158 0.1098643543 0.3625839019 0.2402798949 -0.2212075333
## 369 370 371 372 373
## 0.1713181523 0.2397639598 -0.0049336607 -0.0281550253 0.1936668508
## 374 375 376 377 378
## 0.0510488619 -0.0366773338 0.0453516411 0.2124427988 -0.0842425665
## 379 380 381 382 383
## -0.1475910204 0.2613032881 0.4406129483 0.2929329946 0.0285230114
## 384 385 386 387 388
## -0.8516842219 -0.6466077640 0.0643124972 0.3300621741 -0.1328908878
## 389 390 391 392 393
## -0.0040689159 0.0836490455 0.1201035464 -0.2848916010 -0.1120599966
## 394 395 396 397 398
## 0.1741114308 -0.0455019076 -0.1282719604 -0.2989890985 -0.0955829816
## 399 400 401 402 403
## -0.3229258781 -0.1414844943 -0.0224640605 0.0163903173 -0.2059367988
## 404 405 406 407 408
## -0.0108878732 0.0297608960 -0.5966058417 0.1068818363 -0.1668787565
## 409 410 411 412 413
## -0.3212534040 -0.0340397134 -0.2767588383 -0.0905960370 -0.4037532477
## 414 415 416 417 418
## 0.4004180760 -0.0392553021 -0.1015704616 0.0915091709 -0.0014145000
## 419 420 421 422 423
## -0.3422415357 -0.5800023946 -0.4098367138 -0.1008842941 -0.7912262945
## 424 425 426 427 428
## -0.4828132137 0.4534928300 -0.2516316402 0.4356903908 0.3157507201
## 429 430 431 432 433
## 0.3771111481 -0.3380409860 0.2885982807 0.1135904777 -0.3249176619
## 434 435 436 437 438
## 0.2982984274 -0.1160524762 -0.6491538797 -0.0172520094 -0.2464148793
## 439 440 441 442 443
## -0.1073706821 0.1893366529 0.5683373929 0.7732573661 -0.4779314841
## 444 445 446 447 448
## -0.1648794824 -0.1764759832 -0.0818705451 -0.0069821860 0.1077607792
## 449 450 451 452 453
## -0.0074397206 -0.4239312945 -0.1583660965 -0.4271888633 0.0762154092
## 454 455 456 457 458
## 0.0585431371 0.1483982242 0.0226254589 0.0501607521 -0.3349673594
## 459 460 461 462 463
## 0.1582890856 0.8308830364 -0.5841289706 -0.0853054910 -0.1196018495
## 464 465 466 467 468
## -0.0893841679 0.3321793116 0.6276016467 -0.1766019878 -0.1547776862
## 469 470 471 472 473
## -0.5477095332 -0.5863557689 0.2084662617 0.0598690552 -0.6016516047
## 474 475 476 477 478
## -0.3189491883 -0.6601332739 1.0700598927 -0.6155057022 0.4270998270
## 479 480 481 482 483
## 0.3987775740 0.3342462321 0.2639813290 0.5856055878 -0.7829444706
## 484 485 486 487 488
## -0.0724945864 0.1459534955 -0.2016262927 0.0100804816 -0.1469747762
## 489 490
## 0.1500310128 -0.0589155599
remove <- list(p =list(mean_precipation = c(1:13),
mean_temp= c(1:13)))
mod_ardl813_weather_hanover <- ardlDlm(log_mean_new_cases ~ log_viral_gene + mean_precipation +
mean_temp,data = full_cases_wastewater_weather_data_hanover_train,
p=13,q=8,
remove = remove)
summary(mod_ardl813_weather_hanover)
##
## Time series regression with "ts" data:
## Start = 14, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.45728 -0.20362 -0.00207 0.23502 1.11040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.419363 0.280402 -1.496 0.13546
## log_viral_gene.t 0.089389 0.030632 2.918 0.00370 **
## log_viral_gene.1 -0.014273 0.041552 -0.343 0.73139
## log_viral_gene.2 -0.047902 0.041530 -1.153 0.24934
## log_viral_gene.3 0.045005 0.042316 1.064 0.28811
## log_viral_gene.4 0.054980 0.042360 1.298 0.19497
## log_viral_gene.5 -0.046908 0.042672 -1.099 0.27224
## log_viral_gene.6 -0.002676 0.042723 -0.063 0.95008
## log_viral_gene.7 -0.027996 0.042641 -0.657 0.51180
## log_viral_gene.8 0.068167 0.042583 1.601 0.11012
## log_viral_gene.9 -0.096333 0.042266 -2.279 0.02312 *
## log_viral_gene.10 0.007339 0.042473 0.173 0.86289
## log_viral_gene.11 0.070184 0.041786 1.680 0.09373 .
## log_viral_gene.12 -0.030315 0.041906 -0.723 0.46981
## log_viral_gene.13 -0.044443 0.030723 -1.447 0.14871
## mean_precipation.t -0.067175 0.042797 -1.570 0.11720
## mean_temp.t 0.001380 0.001415 0.975 0.33002
## log_mean_new_cases.1 0.448963 0.046777 9.598 < 2e-16 ***
## log_mean_new_cases.2 0.116268 0.050941 2.282 0.02293 *
## log_mean_new_cases.3 0.026562 0.051085 0.520 0.60335
## log_mean_new_cases.4 0.142631 0.050922 2.801 0.00531 **
## log_mean_new_cases.5 0.075016 0.050778 1.477 0.14028
## log_mean_new_cases.6 0.069760 0.050730 1.375 0.16978
## log_mean_new_cases.7 0.158127 0.050821 3.111 0.00198 **
## log_mean_new_cases.8 -0.082524 0.047092 -1.752 0.08038 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3781 on 452 degrees of freedom
## Multiple R-squared: 0.9044, Adjusted R-squared: 0.8993
## F-statistic: 178.1 on 24 and 452 DF, p-value: < 2.2e-16
f_ardl813_weather_hanover <- forecast(mod_ardl813_weather_hanover, x= t(full_cases_wastewater_weather_data_hanover_test[,c(7,4,5)]),h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl813_weather_hanover$forecasts)
## [1] 0.3580285
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_ardl813_weather_hanover$forecasts)
## [1] 0.2687249
checkresiduals(mod_ardl813_weather_hanover)
## Time Series:
## Start = 14
## End = 490
## Frequency = 1
## 14 15 16 17 18 19
## 0.201136122 0.138087477 -0.287201701 -0.052076308 -0.002067104 0.080752066
## 20 21 22 23 24 25
## 0.196961759 0.203818849 0.252163953 -0.004275758 -0.088601919 -0.041525351
## 26 27 28 29 30 31
## -0.279265664 0.673548659 -0.200156773 0.380983246 -0.419303963 0.170739590
## 32 33 34 35 36 37
## -0.008480237 -0.074105360 0.262313772 0.590101529 0.230448808 -0.127015624
## 38 39 40 41 42 43
## -0.185533122 0.092135946 0.002827951 0.205420878 -0.106952183 -0.232183946
## 44 45 46 47 48 49
## 0.105172602 -0.157873823 -0.175422760 -0.296723711 0.062225637 -0.405596962
## 50 51 52 53 54 55
## 0.208074750 -0.189459158 -0.422882323 0.250822301 -0.202250881 0.238969847
## 56 57 58 59 60 61
## 0.407329096 0.238002899 0.042943606 0.012616767 0.112949498 0.108307049
## 62 63 64 65 66 67
## 0.287610278 0.097235278 -0.119365064 -0.292965861 0.646300651 0.233041434
## 68 69 70 71 72 73
## 0.108225938 -0.183650869 0.394297110 -0.074574761 -0.081176872 0.102991276
## 74 75 76 77 78 79
## -0.228935215 0.085932428 0.289552852 0.223318053 0.160936526 -0.051270758
## 80 81 82 83 84 85
## 0.366391729 0.276705565 0.093526577 0.034588297 -0.073395941 0.238345497
## 86 87 88 89 90 91
## -0.125824397 0.208149546 -0.406394181 -0.108965029 -0.273728070 0.136231699
## 92 93 94 95 96 97
## -0.378166440 -0.099871049 -0.359419933 0.287944665 -0.001975522 -0.329627686
## 98 99 100 101 102 103
## 0.138636745 0.216954032 0.140477926 0.065264260 0.031449975 -0.009382325
## 104 105 106 107 108 109
## 0.346179115 -0.260776021 -1.194967263 0.658861532 -0.211611811 0.237279301
## 110 111 112 113 114 115
## -0.043414688 0.382738622 0.543716848 -1.092734080 0.726163118 0.199963668
## 116 117 118 119 120 121
## 0.015315413 0.013144010 0.123717776 -0.644581974 0.264365668 0.038524782
## 122 123 124 125 126 127
## -0.495315592 -0.049253232 -1.073232032 0.425858627 0.269940446 -0.580280971
## 128 129 130 131 132 133
## 0.525727733 -0.136450551 0.464550899 -0.154115232 0.070464148 -0.514645736
## 134 135 136 137 138 139
## -0.214299764 0.256107546 -0.898879542 -0.499129551 0.692321979 0.279988959
## 140 141 142 143 144 145
## -0.321280046 -0.002779462 -0.683003447 0.899510819 -0.779246851 0.261569553
## 146 147 148 149 150 151
## -0.300546369 0.127442553 0.215723413 -0.296639526 -0.258501183 0.060109899
## 152 153 154 155 156 157
## -0.105671274 0.083230131 0.212014478 0.156010293 -0.339707220 -0.073604116
## 158 159 160 161 162 163
## -0.203624074 -0.019442747 0.001836799 0.515646723 0.373333552 -0.578922900
## 164 165 166 167 168 169
## -0.008737259 -0.181595671 -0.001515983 0.067523034 0.248451690 0.201127717
## 170 171 172 173 174 175
## -0.264205286 -0.109144067 -0.022961651 -0.078079936 -0.213062362 0.720606157
## 176 177 178 179 180 181
## -0.083290794 -0.494896207 -0.371894574 -0.483660149 0.430160756 -0.211883600
## 182 183 184 185 186 187
## -0.045688610 0.276527020 -0.348842787 0.492620205 -0.042111165 -0.409819929
## 188 189 190 191 192 193
## -0.251821047 0.010656120 0.712616961 -0.523461543 -0.615014874 1.110403695
## 194 195 196 197 198 199
## -0.014583121 0.571812581 -0.442311880 -0.644113868 -0.690624437 0.518256999
## 200 201 202 203 204 205
## 0.055437912 0.840896214 0.329558634 0.741237453 0.798165085 0.145797863
## 206 207 208 209 210 211
## 0.029371756 -0.134060295 0.100602542 -0.006421255 -0.084638792 0.271700945
## 212 213 214 215 216 217
## 0.118366107 0.237147627 -0.070898701 -0.020481936 0.425791827 0.022858482
## 218 219 220 221 222 223
## 0.009195603 0.061822830 0.095837710 -0.108671559 -0.178355271 0.093770262
## 224 225 226 227 228 229
## -0.168693144 0.185554010 0.195521816 -0.052467983 0.012566510 0.302946097
## 230 231 232 233 234 235
## 0.018929675 -0.240448437 0.054451207 0.596966907 0.587624677 0.269479821
## 236 237 238 239 240 241
## 0.353936850 -0.189716977 -0.564800048 -0.264751388 -0.129735335 0.064532765
## 242 243 244 245 246 247
## 0.206307276 -0.104994852 -0.245976041 -0.158197274 -0.313203433 -0.834779661
## 248 249 250 251 252 253
## 0.382023981 0.014486566 -0.169483022 0.109822710 -0.271066626 0.060968286
## 254 255 256 257 258 259
## 0.341855818 -0.256220606 -0.143319093 -0.139008526 0.081151818 -0.133540718
## 260 261 262 263 264 265
## -0.306678722 -0.121694844 0.074540120 0.013141469 -0.067008563 -0.457237010
## 266 267 268 269 270 271
## -0.067574260 -0.100925239 -0.129015371 -0.156833000 -0.256050815 -0.459169970
## 272 273 274 275 276 277
## 0.235023648 -0.225913223 -0.718260283 0.364475466 0.048532776 -0.411747868
## 278 279 280 281 282 283
## 0.342284523 -0.172462818 0.274749027 -0.264491195 -0.026342688 -0.115555722
## 284 285 286 287 288 289
## -0.016207610 0.120630746 0.197674423 -0.283883035 -0.323017563 -0.022510262
## 290 291 292 293 294 295
## 0.129532923 -1.457281795 -0.764307068 -0.567108209 0.716424049 -0.435110044
## 296 297 298 299 300 301
## -0.058296793 -0.116154673 0.430229801 -0.696427057 0.289145115 -0.419874468
## 302 303 304 305 306 307
## 0.011354745 -0.130209319 0.447628080 -0.089265685 -0.580598888 -0.058478793
## 308 309 310 311 312 313
## 0.361585196 0.066476608 0.653090805 -0.408456876 -0.147649861 0.180428953
## 314 315 316 317 318 319
## 0.575637124 0.836994109 -0.333249395 0.190716004 0.412107404 0.283578329
## 320 321 322 323 324 325
## -0.016312212 -0.526851465 -0.065648506 0.546956601 -0.301534385 -0.290340997
## 326 327 328 329 330 331
## -0.119437892 -1.219048720 -0.041767727 0.645666082 0.872459278 0.512147959
## 332 333 334 335 336 337
## 0.233492431 -0.100141147 0.291078186 -0.145454202 -0.203465597 0.288031194
## 338 339 340 341 342 343
## -0.006316665 -0.244808778 0.522306990 0.245303856 -0.772500320 0.530178152
## 344 345 346 347 348 349
## 0.368787544 0.145866689 0.194394063 -0.082636688 0.257898695 0.355292668
## 350 351 352 353 354 355
## 0.201247279 0.433212991 0.409306787 -0.127008631 0.558126178 0.410382286
## 356 357 358 359 360 361
## -0.465281294 -0.676389134 0.599785306 0.804669944 0.704680347 0.528277690
## 362 363 364 365 366 367
## 0.617289299 -0.151048840 -0.293539878 0.176683161 0.453347991 0.333282713
## 368 369 370 371 372 373
## 0.001341451 0.427572339 0.296529191 -0.130455306 -0.112611804 0.182802995
## 374 375 376 377 378 379
## 0.065393493 0.075535696 0.177224380 0.268863200 -0.186241531 -0.213737583
## 380 381 382 383 384 385
## 0.293545665 0.442884534 0.285443532 0.052334772 -0.831367730 -0.625694299
## 386 387 388 389 390 391
## 0.084921139 0.343263761 -0.149265118 -0.082853122 0.034850680 0.050853476
## 392 393 394 395 396 397
## -0.441726859 -0.247528651 0.052062754 -0.143201551 -0.073544362 -0.210568237
## 398 399 400 401 402 403
## -0.133618834 -0.419890845 -0.211861999 -0.072464269 -0.010828214 -0.255019683
## 404 405 406 407 408 409
## -0.051056485 -0.074760817 -0.716624693 0.019198934 -0.228725922 -0.381313585
## 410 411 412 413 414 415
## -0.062253388 -0.281194110 -0.103963640 -0.458847488 0.320646937 -0.096959498
## 416 417 418 419 420 421
## -0.203002835 0.043335269 -0.031027742 -0.445895404 -0.584398517 -0.396233642
## 422 423 424 425 426 427
## -0.055875259 -0.839551861 -0.459803673 0.489707399 -0.384158699 0.349108584
## 428 429 430 431 432 433
## 0.190325628 0.224260317 -0.462528163 0.237546874 0.172775401 -0.302324280
## 434 435 436 437 438 439
## 0.312776588 0.065204992 -0.553719692 0.048348811 -0.168060104 -0.027716001
## 440 441 442 443 444 445
## 0.172597293 0.546265573 0.858338947 -0.549158098 -0.101947165 -0.064536997
## 446 447 448 449 450 451
## -0.116491862 0.012665841 0.202839309 0.062830286 -0.370730330 -0.130823011
## 452 453 454 455 456 457
## -0.409409460 -0.055611840 -0.076415875 0.089932454 -0.032477311 0.070029395
## 458 459 460 461 462 463
## -0.281919760 0.151533870 0.720220560 -0.651109815 -0.112179683 -0.105471991
## 464 465 466 467 468 469
## 0.035219815 0.496528859 0.674641429 -0.169244575 -0.154525846 -0.601122163
## 470 471 472 473 474 475
## -0.452664284 0.273196986 0.173809463 -0.416161405 -0.236797656 -0.644270571
## 476 477 478 479 480 481
## 1.031363946 -0.779339802 0.332166184 0.395576233 0.361184263 0.351064263
## 482 483 484 485 486 487
## 0.605743205 -0.829530446 0.015548050 0.186549694 0.092414220 0.194067125
## 488 489 490
## -0.115963642 0.346188494 0.007436453
#plots#
mod_ardl92_acf <- ggAcf(residuals(mod_ardl92)) + theme_bw()
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -2.396407e-02 -3.976665e-02 2.253188e-02 1.126186e-02 -3.456715e-05
## 15 16 17 18 19
## -1.584383e-01 -1.087522e-01 -5.617950e-02 -2.259314e-02 -4.996504e-02
## 20 21 22 23 24
## 1.568234e-01 1.735783e-02 -2.082497e-01 2.457965e-01 -5.157538e-02
## 25 26 27 28 29
## 2.722065e-03 -2.621960e-01 2.818996e-01 -2.949834e-01 -3.035126e-01
## 30 31 32 33 34
## 1.661684e-01 -4.430982e-02 5.693436e-02 1.717116e-01 1.064284e-01
## 35 36 37 38 39
## -1.529803e-01 -2.945897e-01 1.263618e-01 -2.567127e-01 -1.473113e-02
## 40 41 42 43 44
## 5.214441e-02 2.746484e-02 -2.552454e-01 -8.854845e-02 -1.247769e-01
## 45 46 47 48 49
## 1.160506e-01 7.937280e-02 -6.261422e-02 9.856974e-02 -2.195059e-01
## 50 51 52 53 54
## 1.127137e-01 -1.766453e-01 -5.426369e-02 -4.002780e-01 -3.406671e-02
## 55 56 57 58 59
## 5.963782e-02 1.016042e-01 2.000816e-01 2.983519e-03 -2.650524e-01
## 60 61 62 63 64
## 1.486018e-01 1.601307e-01 -1.384878e-01 7.687082e-02 -4.141107e-02
## 65 66 67 68 69
## 1.098705e-01 -3.128669e-02 6.173563e-02 1.494617e-01 7.418673e-02
## 70 71 72 73 74
## 1.644328e-01 4.680422e-01 2.262063e-02 -1.274640e-01 5.006964e-02
## 75 76 77 78 79
## -3.068078e-01 8.782886e-02 -4.406198e-02 -2.869990e-03 5.181883e-03
## 80 81 82 83 84
## 5.072444e-02 -2.090606e-01 1.372967e-01 -1.820851e-01 -1.857852e-02
## 85 86 87 88 89
## 3.443533e-01 -2.852786e-01 2.303650e-02 2.023233e-01 -2.091241e-01
## 90 91 92 93 94
## -5.177255e-01 -1.381966e-01 3.400566e-01 3.701602e-01 2.276316e-01
## 95 96 97 98 99
## 1.177870e-01 3.214996e-01 1.667340e-01 -1.459042e-03 2.712643e-01
## 100 101 102 103 104
## -3.993105e-01 -1.274003e-02 -2.554181e-01 -1.053282e-01 -1.625378e-01
## 105 106 107 108 109
## 5.634557e-02 -2.966006e-02 1.075129e-01 -6.818631e-02 3.926711e-02
## 110 111 112 113 114
## 1.489118e-01 -5.768349e-02 1.701619e-01 2.698320e-01 4.012499e-03
## 115 116 117 118 119
## 6.400294e-03 -2.979161e-02 -1.944667e-01 5.016915e-02 -2.560521e-01
## 120 121 122 123 124
## 3.215355e-01 -2.638250e-01 1.665216e-01 -2.162241e-02 1.748811e-01
## 125 126 127 128 129
## -1.494302e-01 1.042969e-02 2.123463e-01 -2.841083e-03 1.362311e-01
## 130 131 132 133 134
## 1.325026e-01 -1.897168e-01 1.637814e-01 -3.943942e-02 1.827401e-02
## 135 136 137 138 139
## -5.139633e-02 2.554954e-01 -1.630690e-01 1.330048e-01 -2.957152e-01
## 140 141 142 143 144
## 1.841674e-01 2.507736e-01 -1.557800e-01 9.174971e-02 -2.204612e-01
## 145 146 147 148 149
## -1.119750e-01 -2.616129e-01 -6.771456e-02 1.873420e-01 -1.271189e+00
## 150 151 152 153 154
## 2.556409e-01 -1.170900e+00 1.055138e-01 4.032973e-01 3.828688e-01
## 155 156 157 158 159
## 5.568852e-01 -2.625216e-01 -3.221344e-01 -3.517223e-01 -2.326498e-01
## 160 161 162 163 164
## -6.413548e-01 1.490695e-01 -8.621020e-02 4.664573e-01 1.604656e-01
## 165 166 167 168 169
## 1.383717e-01 -2.395036e-02 3.262965e-01 -1.042147e-01 -3.213268e-01
## 170 171 172 173 174
## -3.663798e-01 -6.002995e-02 -7.778285e-01 9.547445e-02 -2.161891e-01
## 175 176 177 178 179
## 4.416636e-01 6.852906e-02 3.004097e-02 -2.704458e-01 -7.407742e-02
## 180 181 182 183 184
## 4.190433e-02 1.797658e-01 -2.287042e-01 -1.620557e+00 7.144359e-01
## 185 186 187 188 189
## 2.002879e-01 1.150878e-01 1.289638e-01 6.242632e-01 2.050394e-01
## 190 191 192 193 194
## 3.527073e-01 -1.933211e-02 7.994148e-02 -3.369943e-01 1.785146e-01
## 195 196 197 198 199
## -2.045247e-01 2.162620e-03 2.513039e-01 -2.552056e-02 3.232862e-01
## 200 201 202 203 204
## -6.735815e-02 3.296637e-01 8.652104e-02 2.380897e-01 4.655643e-01
## 205 206 207 208 209
## 8.662858e-02 -1.184034e-02 -9.723711e-02 2.729274e-01 8.313439e-03
## 210 211 212 213 214
## 1.015981e-01 -5.016132e-02 2.061002e-01 -5.190664e-02 1.400110e-02
## 215 216 217 218 219
## 2.209761e-01 -1.501411e-01 5.880174e-02 1.781954e-01 5.708528e-02
## 220 221 222 223 224
## 1.981210e-02 1.167935e-02 1.602544e-01 7.165049e-03 -3.680604e-02
## 225 226 227 228 229
## -5.092278e-03 1.754901e-01 -3.829182e-02 1.375325e-01 1.482769e-01
## 230 231 232 233 234
## 5.776840e-02 1.493228e-01 -9.650623e-02 2.228080e-01 -4.609739e-02
## 235 236 237 238 239
## 9.670582e-02 1.313394e-01 1.672115e-01 5.662791e-01 -3.761859e-01
## 240 241 242 243 244
## -6.367110e-02 -2.081374e-01 9.186764e-02 2.436832e-01 3.653342e-03
## 245 246 247 248 249
## -6.807823e-02 -6.105565e-01 -1.620877e+00 9.680602e-01 1.192657e-03
## 250 251 252 253 254
## -9.628339e-02 1.545319e-01 3.129851e-01 -1.631988e-01 2.493072e-01
## 255 256 257 258 259
## -4.769542e-01 -8.771902e-02 -2.167812e-03 -1.056218e-02 1.022641e-01
## 260 261 262 263 264
## -2.346255e-01 1.379507e-02 -2.023609e-01 -1.173748e-01 -2.047266e-01
## 265 266 267 268 269
## 6.049889e-02 -2.346834e-01 -4.229977e-01 3.988999e-01 -9.839163e-02
## 270 271 272 273 274
## -2.135352e-02 7.741357e-02 1.877729e-02 2.034479e-01 -4.268264e-01
## 275 276 277 278 279
## -1.360064e-01 -2.454923e-01 5.370585e-02 -6.652115e-02 7.476438e-01
## 280 281 282 283 284
## -5.191479e-01 4.549196e-01 -2.347329e-01 2.828300e-02 4.456982e-01
## 285 286 287 288 289
## 3.968121e-02 -4.771259e-01 -2.831081e-01 -7.737644e-01 3.006624e-01
## 290 291 292 293 294
## -1.023992e-01 1.395710e-01 -2.364213e+00 -3.909424e-01 1.450096e+00
## 295 296 297 298 299
## -2.085535e-01 2.979523e-01 6.068575e-01 3.951824e-01 2.037335e-01
## 300 301 302 303 304
## 8.261871e-02 -3.236322e-01 -5.990560e-01 -2.930634e-01 -2.168600e-01
## 305 306 307 308 309
## -4.583283e-02 -3.267313e-01 1.914202e-01 -1.029380e-01 4.824966e-01
## 310 311 312 313 314
## -2.567830e-01 -9.254083e-01 5.238682e-01 -2.883445e-01 4.218525e-01
## 315 316 317 318 319
## -1.152390e-01 2.896990e-01 2.318420e-01 -4.225929e-02 1.206934e-01
## 320 321 322 323 324
## -1.258189e-02 8.128629e-02 5.362193e-01 3.580403e-02 5.387543e-02
## 325 326 327 328 329
## -1.426912e-01 -2.952867e-01 -7.912501e-01 1.631587e-01 4.219926e-01
## 330 331 332 333 334
## 6.565432e-02 4.054452e-01 2.009018e-01 4.716507e-01 2.343397e-02
## 335 336 337 338 339
## 2.490811e-01 5.407757e-02 2.453663e-01 -2.296027e-01 3.777055e-02
## 340 341 342 343 344
## -2.720543e-01 -4.027320e-01 2.307273e-01 -3.164816e-02 2.747526e-01
## 345 346 347 348 349
## -4.497552e-03 -1.574489e-01 -4.906954e-02 8.772337e-02 1.370770e-01
## 350 351 352 353 354
## 4.529530e-01 1.906016e-01 1.525708e-01 3.284963e-01 3.650998e-01
## 355 356 357 358 359
## 5.396324e-01 -3.074325e-01 -5.349434e-01 8.777813e-01 9.443478e-01
## 360 361 362 363 364
## 7.003203e-01 4.952868e-01 5.047689e-01 -1.918388e-01 5.261175e-02
## 365 366 367 368 369
## -1.077546e-01 1.598769e-01 4.668144e-01 3.266047e-01 2.771328e-01
## 370 371 372 373 374
## 1.589788e-01 1.313453e-02 -6.308058e-01 3.184335e-01 -6.444854e-03
## 375 376 377 378 379
## 1.939464e-01 1.715339e-01 1.996648e-01 -3.091449e-01 -1.296596e+00
## 380 381 382 383 384
## 1.088063e-01 5.960841e-01 2.713044e-01 2.329620e-01 -8.556874e-01
## 385 386 387 388 389
## -9.022326e-01 4.009147e-01 5.146857e-01 -9.337388e-02 1.724957e-01
## 390 391 392 393 394
## 1.810539e-01 1.784066e-01 -8.606756e-01 -2.221742e-01 1.713428e-01
## 395 396 397 398 399
## -1.589677e-01 -2.242434e-03 6.841561e-02 4.039676e-02 1.309074e-01
## 400 401 402 403 404
## -1.937431e-01 -1.420454e-01 -2.128705e-01 1.629227e-02 -2.543536e-01
## 405 406 407 408 409
## -2.542008e-01 5.524668e-03 3.713062e-02 -3.802828e-02 -8.559204e-02
## 410 411 412 413 414
## -1.088547e-01 9.989792e-02 -1.654432e-01 -3.312310e-01 2.208590e-01
## 415 416 417 418 419
## -1.385087e-01 -2.478310e-01 -2.713380e-01 -1.457082e-01 -6.735750e-02
## 420 421 422 423 424
## -5.499413e-01 1.577297e-02 -2.629274e-01 -2.215989e-01 1.088316e-01
## 425 426 427 428 429
## 1.518798e-01 -7.800507e-01 4.120184e-02 8.104201e-02 1.116859e-01
## 430 431 432 433 434
## 6.589971e-02 -5.915863e-01 3.969890e-01 -1.167412e-01 5.200500e-02
## 435 436 437 438 439
## -1.569589e-01 6.584974e-02 -5.131337e-01 1.382272e-01 -1.724006e-01
## 440 441 442 443 444
## -9.139437e-02 -9.756700e-02 4.205117e-01 9.049092e-02 -4.838474e-01
## 445 446 447 448 449
## 7.527956e-03 3.232683e-01 -1.284454e-01 -3.784562e-01 -9.697398e-02
## 450 451 452 453 454
## -3.759760e-01 3.639162e-01 -2.447045e-01 -3.919063e-02 5.256440e-01
## 455 456 457 458 459
## -1.279611e-01 2.734360e-01 6.062632e-02 -2.399165e-01 3.003080e-01
## 460 461 462 463 464
## -4.265930e-02 5.641235e-02 3.142238e-01 2.458586e-02 -1.890712e-01
## 465 466 467 468 469
## 2.477738e-01 2.543826e-01 8.183976e-02 -1.401468e-01 3.270317e-01
## 470 471 472 473 474
## -8.675708e-02 -2.404920e-02 1.507883e-01 -1.698617e-01 -3.771766e-02
## 475 476 477 478 479
## 9.785553e-02 7.054171e-02 3.302712e-01 -2.662845e-01 8.830143e-03
## 480 481 482 483 484
## 2.716887e-03 -1.649914e-01 1.160813e-01 1.064102e-01 -1.588147e-01
## 485 486 487 488 489
## 1.602108e-01 3.967555e-02 3.183249e-02 2.427844e-01 -4.431468e-03
## 490
## 2.543166e-01
mod_ardl92_meck_acf <- ggAcf(residuals(mod_ardl92_meck)) + theme_bw()
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -3.092371e-02 1.163238e-02 1.252001e-02 1.014782e-01 2.836953e-02
## 15 16 17 18 19
## 2.833400e-02 -1.696518e-03 -1.227269e-01 -1.590525e-01 -3.045078e-02
## 20 21 22 23 24
## 2.184542e-01 5.078416e-02 -3.255922e-02 -1.214547e-01 2.311235e-01
## 25 26 27 28 29
## 4.023654e-02 -2.353277e-01 -8.977339e-02 1.961115e-01 5.112010e-03
## 30 31 32 33 34
## -3.149867e-02 1.427563e-02 -2.207462e-01 -2.851758e-02 -2.929289e-01
## 35 36 37 38 39
## 3.177582e-01 4.487638e-02 -9.499900e-02 -8.387231e-02 -2.265090e-01
## 40 41 42 43 44
## 8.259352e-02 9.959311e-02 -8.641751e-02 -1.764461e-01 1.229113e-01
## 45 46 47 48 49
## -7.265117e-02 -2.519822e-01 9.349147e-02 -2.707908e-01 3.195785e-01
## 50 51 52 53 54
## -2.050264e-01 -3.964405e-01 1.363230e-01 1.925282e-02 2.139667e-02
## 55 56 57 58 59
## -1.014455e-01 -1.146824e-01 3.385559e-01 -3.207601e-01 1.507240e-01
## 60 61 62 63 64
## -1.071141e+00 -2.682274e-01 2.178915e-01 -5.722560e-01 6.045407e-01
## 65 66 67 68 69
## 3.489794e-01 2.040119e-01 -3.519632e-02 2.839743e-01 2.117074e-01
## 70 71 72 73 74
## 3.177930e-01 -4.062772e-02 -6.585365e-02 -2.198761e-01 4.218497e-01
## 75 76 77 78 79
## -1.655438e-01 4.272526e-01 3.326260e-01 3.096256e-01 -1.568450e-02
## 80 81 82 83 84
## -6.525427e-02 -1.434785e-01 -3.334671e-01 -2.611591e-02 -4.666716e-02
## 85 86 87 88 89
## 3.474433e-01 -2.150304e-01 3.881112e-01 2.499551e-02 2.028181e-01
## 90 91 92 93 94
## -2.367724e-01 -8.491285e-02 1.206571e-02 -3.959261e-01 3.882358e-02
## 95 96 97 98 99
## -2.155568e-01 1.809715e-01 8.645893e-02 2.824313e-03 -1.786669e-02
## 100 101 102 103 104
## -8.591058e-02 2.274223e-01 -1.068923e-01 -3.708266e-01 3.465886e-01
## 105 106 107 108 109
## -4.702015e-01 6.073526e-01 -6.934208e-02 -1.380305e-01 1.090499e-01
## 110 111 112 113 114
## -3.081340e-01 9.294370e-02 2.802856e-01 -1.150670e-01 -4.287394e-02
## 115 116 117 118 119
## -1.069286e-01 -4.091438e-01 3.187158e-01 -3.036462e-01 -8.434482e-02
## 120 121 122 123 124
## -1.245349e-01 4.561678e-02 -1.409853e-01 -2.357035e-02 -3.462645e-01
## 125 126 127 128 129
## -4.734365e-03 3.363099e-01 -2.809807e-01 -6.658337e-01 -1.931057e-01
## 130 131 132 133 134
## -8.923531e-01 9.462148e-02 -1.521770e-01 7.699534e-01 7.831224e-02
## 135 136 137 138 139
## 1.447998e-01 -2.591512e-01 -2.804563e-01 1.452160e-01 -5.340732e-01
## 140 141 142 143 144
## -1.774752e-01 3.831458e-01 -2.355669e-01 -5.379080e-01 4.430436e-01
## 145 146 147 148 149
## 4.268551e-01 7.313508e-02 8.329347e-02 -2.276817e-01 -3.157568e-01
## 150 151 152 153 154
## 9.449980e-01 -1.127343e-02 -7.474956e-01 -3.350319e-01 6.629206e-01
## 155 156 157 158 159
## -3.926999e-01 -2.283320e-01 -2.171595e-01 3.702117e-01 2.552329e-01
## 160 161 162 163 164
## -3.746085e-01 3.234608e-01 3.548603e-01 3.353210e-01 1.897544e-01
## 165 166 167 168 169
## -3.546162e-01 -2.689742e-01 -1.656706e-01 3.926646e-01 -5.638034e-01
## 170 171 172 173 174
## -6.236650e-01 -3.644881e-01 2.419904e-01 6.867030e-02 -7.785484e-01
## 175 176 177 178 179
## 3.596520e-01 2.556221e-01 -2.183095e-01 5.990763e-02 -4.009686e-01
## 180 181 182 183 184
## 9.059714e-01 2.544917e-01 1.393752e-01 -4.475876e-01 5.457393e-02
## 185 186 187 188 189
## -2.374567e-01 8.340786e-02 4.492369e-01 4.403853e-01 5.910953e-01
## 190 191 192 193 194
## 2.577866e-01 -1.954837e-01 1.473030e-01 -1.985440e-01 -4.717432e-02
## 195 196 197 198 199
## 7.214516e-02 -1.357494e-02 7.170069e-01 -1.940442e-02 1.830457e-01
## 200 201 202 203 204
## 1.607166e-01 1.394537e-01 2.803610e-01 1.726479e-01 1.823049e-01
## 205 206 207 208 209
## 3.561684e-02 -9.836023e-02 1.927115e-01 6.261834e-02 -1.391065e-02
## 210 211 212 213 214
## 1.735067e-01 1.859842e-01 7.134149e-02 -1.744462e-01 -5.452612e-02
## 215 216 217 218 219
## 1.558357e-01 -3.467078e-02 -1.510130e-01 1.601537e-01 -2.934839e-02
## 220 221 222 223 224
## 5.364477e-02 1.838195e-01 3.012772e-02 9.895059e-02 -2.495102e-01
## 225 226 227 228 229
## -1.737132e-02 -1.475369e-02 1.207811e-01 8.583218e-02 1.213871e-01
## 230 231 232 233 234
## 1.855354e-01 4.753981e-02 1.866039e-01 1.354519e-01 -1.621541e-01
## 235 236 237 238 239
## -1.476087e-01 -9.523335e-03 1.469191e-01 -5.875478e-02 -6.073574e-02
## 240 241 242 243 244
## 1.394707e-01 -9.513615e-02 -2.445320e-01 8.757945e-02 -2.934725e-02
## 245 246 247 248 249
## -9.233432e-02 2.892464e-02 -8.366786e-01 5.078695e-01 2.107009e-01
## 250 251 252 253 254
## 2.047745e-01 8.030800e-02 1.051612e-01 -1.453955e-01 9.064731e-02
## 255 256 257 258 259
## -1.313186e-01 -4.096315e-01 -1.006922e-02 7.446587e-02 -1.236577e-01
## 260 261 262 263 264
## -1.928842e-01 6.074715e-02 -1.290528e-01 -2.034470e-01 7.606261e-02
## 265 266 267 268 269
## -1.389784e-01 -2.766717e-02 -2.661200e-01 1.163460e-01 -2.396346e-01
## 270 271 272 273 274
## 4.097262e-01 -4.466364e-02 1.329093e-01 -1.376155e-01 -3.050477e-01
## 275 276 277 278 279
## 6.348342e-02 -1.009835e-01 -3.900220e-01 -1.174700e-01 1.093365e-01
## 280 281 282 283 284
## -2.734615e-01 4.514930e-02 -1.382426e-02 -1.349219e-01 1.037062e-01
## 285 286 287 288 289
## -1.236246e-01 1.722392e-01 6.008186e-02 -1.184771e-01 -1.498106e-01
## 290 291 292 293 294
## -3.679851e-01 -1.146621e-01 -1.211610e+00 -2.829368e-01 6.819258e-01
## 295 296 297 298 299
## 5.833887e-01 5.790571e-02 1.464892e-01 3.321741e-01 -3.720783e-01
## 300 301 302 303 304
## 1.564222e-01 1.168640e-01 -2.581056e-01 1.968431e-02 2.939600e-02
## 305 306 307 308 309
## -5.594626e-01 2.314759e-01 -7.625572e-02 1.770047e-01 6.695224e-02
## 310 311 312 313 314
## 1.017863e-01 -2.388097e-01 2.251281e-03 -3.007638e-02 6.243413e-02
## 315 316 317 318 319
## 1.010172e-01 2.798638e-01 -1.123650e-01 1.994614e-01 2.516946e-02
## 320 321 322 323 324
## 1.304755e-02 -9.812070e-02 1.101769e-01 -5.688409e-02 -1.611528e-01
## 325 326 327 328 329
## 2.100385e-01 -4.400001e-02 -5.062325e-01 2.867265e-01 8.064437e-01
## 330 331 332 333 334
## 3.036679e-02 3.228944e-01 -6.375375e-02 2.207628e-01 3.847121e-02
## 335 336 337 338 339
## 4.157262e-01 -1.862650e-01 -2.152798e-01 1.450628e-01 -1.573700e-01
## 340 341 342 343 344
## -3.183065e-02 -9.206769e-02 1.181346e-01 7.614366e-02 2.500905e-02
## 345 346 347 348 349
## 3.277367e-01 7.651524e-03 2.772196e-01 2.234536e-01 3.496113e-01
## 350 351 352 353 354
## 1.703349e-01 2.441747e-01 2.443558e-01 3.307703e-01 4.035216e-01
## 355 356 357 358 359
## 3.452711e-01 -2.891394e-02 -7.149718e-01 7.580044e-01 6.009496e-01
## 360 361 362 363 364
## 5.801873e-01 4.424346e-01 4.607344e-01 -7.361956e-02 -2.887587e-01
## 365 366 367 368 369
## 2.649712e-01 2.405537e-01 2.796954e-01 2.958525e-01 2.132516e-01
## 370 371 372 373 374
## -2.750058e-02 -2.824429e-01 -1.764350e-01 2.016469e-01 -1.351666e-02
## 375 376 377 378 379
## 1.020631e-01 6.526443e-02 1.155335e-01 -2.553103e-01 -1.762980e+00
## 380 381 382 383 384
## 2.101670e-01 5.359992e-01 4.782681e-01 3.562092e-01 -8.033185e-02
## 385 386 387 388 389
## -3.883561e-01 2.627346e-02 7.952609e-02 -2.607643e-01 -1.175277e-01
## 390 391 392 393 394
## -5.857509e-02 -1.150789e-01 -2.598925e-01 -4.213645e-02 1.198930e-01
## 395 396 397 398 399
## -2.661433e-01 1.489386e-01 -2.024840e-01 7.704819e-02 -2.903232e-01
## 400 401 402 403 404
## -1.647626e-01 1.643158e-01 -1.258556e-01 7.388809e-02 -7.547620e-02
## 405 406 407 408 409
## 4.738201e-02 -1.695564e-01 -5.873658e-01 1.816129e-01 -3.658345e-01
## 410 411 412 413 414
## -1.541965e-01 -1.419844e-01 8.592332e-03 -7.089878e-03 1.165630e-01
## 415 416 417 418 419
## -6.272235e-02 -5.778883e-02 -2.247626e-01 -2.778469e-01 4.572784e-01
## 420 421 422 423 424
## -6.440206e-01 -1.030302e+00 3.249665e-01 -4.085808e-01 -1.785736e-01
## 425 426 427 428 429
## 7.035872e-02 -3.651298e-01 -5.662069e-01 7.933071e-01 -4.768814e-01
## 430 431 432 433 434
## -2.922878e-01 -2.685913e-01 -7.243048e-01 1.725235e-01 1.543828e-01
## 435 436 437 438 439
## -1.620727e-01 -4.584507e-01 5.191641e-02 9.345671e-01 -3.536851e-01
## 440 441 442 443 444
## 6.352328e-02 -3.436279e-01 1.305824e-01 2.842651e-01 -3.008418e-01
## 445 446 447 448 449
## 1.386451e-01 1.215209e-01 -2.017925e-01 -4.699615e-01 4.751846e-01
## 450 451 452 453 454
## -7.258056e-01 1.091502e+00 1.442230e-01 -1.525797e-02 -4.045037e-01
## 455 456 457 458 459
## 1.532905e-02 -3.790277e-02 8.403449e-02 -3.366523e-02 2.058621e-01
## 460 461 462 463 464
## 2.752573e-01 -1.232036e-01 -5.652366e-01 4.062207e-01 4.750853e-01
## 465 466 467 468 469
## 1.755680e-01 3.300130e-01 3.608029e-01 -3.666815e-01 -5.185949e-02
## 470 471 472 473 474
## -6.779433e-01 3.216355e-01 7.937263e-02 5.339369e-02 1.819193e-01
## 475 476 477 478 479
## -1.874273e-01 -3.059841e-01 8.937394e-03 4.802756e-01 -1.195863e-01
## 480 481 482 483 484
## 2.334788e-01 -2.064050e-02 -4.314131e-02 6.413132e-02 -4.859655e-03
## 485 486 487 488 489
## 1.579740e-01 -5.826499e-02 1.890077e-01 6.867093e-02 -4.940313e-05
## 490
## 1.385353e-01
mod_ardl92_hanover_acf <- ggAcf(residuals(mod_ardl92_hanover)) + theme_bw()
## Time Series:
## Start = 10
## End = 490
## Frequency = 1
## 10 11 12 13 14
## -0.2937247715 0.0725525051 0.2357132291 0.0428823729 0.2024050180
## 15 16 17 18 19
## 0.1383610625 -0.2676940703 -0.0134268985 -0.0117135696 0.0764144973
## 20 21 22 23 24
## 0.1981303419 0.2113455282 0.2379975457 0.0051074184 -0.0491099861
## 25 26 27 28 29
## -0.1261627848 -0.2905892448 0.6591943825 -0.2276926085 0.3194060555
## 30 31 32 33 34
## -0.4551185306 0.1445597583 -0.0568366994 -0.0627825150 0.2938045965
## 35 36 37 38 39
## 0.3709020208 0.2960118006 -0.0942220382 -0.1734517743 0.0226241743
## 40 41 42 43 44
## 0.0270041027 0.1869636936 -0.2392370427 -0.3142958568 0.2411378355
## 45 46 47 48 49
## -0.0771738354 -0.1404487333 -0.3677277543 0.0431663383 -0.4316978812
## 50 51 52 53 54
## 0.2531292334 -0.1388129807 -0.4180790801 0.3174781199 -0.1916208740
## 55 56 57 58 59
## 0.1987007527 0.3663651337 0.2555273155 0.0239482523 -0.0530943676
## 60 61 62 63 64
## 0.1176959277 0.0485663629 0.1937034479 0.0685978034 -0.1774245281
## 65 66 67 68 69
## -0.4345144209 0.6653127842 0.1917715091 0.1800176281 -0.2190088185
## 70 71 72 73 74
## 0.4411357528 0.0434507919 -0.0425528122 0.0906556734 -0.1789678336
## 75 76 77 78 79
## 0.1817007557 0.4857756943 0.2444219798 0.1366642375 0.1156306111
## 80 81 82 83 84
## 0.4289515301 0.3184282752 0.1221898253 -0.0488892873 -0.1376011723
## 85 86 87 88 89
## 0.2397033861 -0.0037757774 0.2027015932 -0.3899420104 -0.0166538988
## 90 91 92 93 94
## -0.2101998536 0.0999245294 -0.2764622533 0.1196021546 -0.1969040255
## 95 96 97 98 99
## 0.4246182427 0.0866703371 -0.2692966292 0.1022241170 0.1845049143
## 100 101 102 103 104
## 0.2844814622 0.0567238754 0.0718908996 -0.0193711583 0.3085424980
## 105 106 107 108 109
## -0.2717931726 -1.1953301375 0.6730721267 -0.1633869109 0.3155728050
## 110 111 112 113 114
## -0.0091031336 0.3984023024 0.5548959808 -1.0566851701 0.7880259146
## 115 116 117 118 119
## 0.0939056670 0.1223389249 0.0491446447 0.1406920939 -0.6743811810
## 120 121 122 123 124
## 0.3197780047 0.2157982532 -0.5256451527 0.0489862102 -1.0499510287
## 125 126 127 128 129
## 0.4394807412 0.3652649330 -0.5195959156 0.3998504377 -0.1191334670
## 130 131 132 133 134
## 0.4433747581 -0.0947424623 0.0832120425 -0.5277903645 -0.1063871747
## 135 136 137 138 139
## 0.2841217598 -0.8616391162 -0.3790968311 0.7288172894 0.5071672677
## 140 141 142 143 144
## -0.2286002821 0.0314926421 -0.6829332184 0.9703729179 -0.7449079747
## 145 146 147 148 149
## 0.2679769867 -0.3756868031 0.2328898204 0.2944174911 -0.4603615280
## 150 151 152 153 154
## -0.2255009541 -0.0717132127 -0.1898146588 0.0234792637 0.3163682613
## 155 156 157 158 159
## 0.2111669824 -0.2559877586 -0.0066921052 -0.1121490904 -0.0041986795
## 160 161 162 163 164
## 0.0424280537 0.3866164312 0.3249911181 -0.4301015712 -0.0217016916
## 165 166 167 168 169
## -0.2131773712 0.0505797912 0.0663116210 0.2714930485 0.2043053345
## 170 171 172 173 174
## -0.3305856683 0.0199390521 -0.0987236863 -0.0879896828 -0.1770255319
## 175 176 177 178 179
## 0.9075754923 -0.1057388530 -0.4752423733 -0.1321610850 -0.3801484525
## 180 181 182 183 184
## 0.5419094734 -0.2656456412 0.1227014611 0.2842934188 -0.3350889685
## 185 186 187 188 189
## 0.5033548382 -0.0068548374 -0.6091154625 -0.2503721300 0.0775616818
## 190 191 192 193 194
## 0.8245964949 -0.3712032240 -0.6583240983 1.1415074891 0.0754030017
## 195 196 197 198 199
## 0.6061736284 -0.2877254417 -0.7529277730 -0.8836332442 0.7384886742
## 200 201 202 203 204
## 0.0897824100 0.7422410308 0.3995787787 0.7494566948 0.8276606603
## 205 206 207 208 209
## 0.1200761219 -0.0654303538 -0.2230863545 0.0274122666 -0.0400149964
## 210 211 212 213 214
## 0.0022512118 0.2936783139 0.0990719213 0.0543947860 -0.0493149906
## 215 216 217 218 219
## -0.0373004111 0.3833824395 0.0185383025 0.0589516846 0.0781896085
## 220 221 222 223 224
## 0.1379129373 -0.0118587807 -0.1957035215 0.1029201034 -0.1096721278
## 225 226 227 228 229
## 0.2728494624 0.2057127592 -0.1336138055 0.0636875549 0.2787792813
## 230 231 232 233 234
## -0.0819055576 -0.2028231242 0.1279166587 0.6104019865 0.5059773785
## 235 236 237 238 239
## 0.2927907643 0.3309247297 -0.2103299644 -0.6020374951 -0.2870039810
## 240 241 242 243 244
## -0.1242200552 0.1387655073 0.1208341292 0.1154879578 -0.1883789764
## 245 246 247 248 249
## -0.1700820686 -0.4658964526 -0.8623299961 0.6775253499 0.0105449122
## 250 251 252 253 254
## -0.0087829510 0.1708893966 -0.2762265336 -0.0240055186 0.3459538609
## 255 256 257 258 259
## -0.1418843551 -0.1564006393 -0.1053706580 0.1066407105 -0.1853499335
## 260 261 262 263 264
## -0.2487433641 -0.2333642650 -0.2727303989 -0.1687733447 -0.0466078025
## 265 266 267 268 269
## -0.3995324342 -0.0677488924 -0.0471187115 -0.0601087398 -0.1041610652
## 270 271 272 273 274
## -0.2367197351 -0.3989378404 0.2484457684 -0.1568777389 -0.7453024532
## 275 276 277 278 279
## 0.3555214858 0.1002671666 -0.3868654278 0.3040895309 -0.2028461658
## 280 281 282 283 284
## 0.1722189512 -0.2332142707 -0.0440658053 -0.3086458206 -0.0504900649
## 285 286 287 288 289
## 0.1012008512 0.1700433893 -0.3481999153 -0.3257685419 0.0074100728
## 290 291 292 293 294
## 0.0341751172 -1.4888343080 -0.7335710249 -0.5480315814 0.7716219916
## 295 296 297 298 299
## -0.3682446885 -0.0486605721 -0.1022491050 0.4153375971 -0.6283894824
## 300 301 302 303 304
## 0.2012134868 -0.5205160486 -0.1192180476 -0.0939335491 0.4307161292
## 305 306 307 308 309
## -0.1346345308 -0.6418514036 -0.1222579844 0.1329938855 0.1042333559
## 310 311 312 313 314
## 0.5206664141 -0.6846115233 -0.3201812611 0.0842644910 0.6126850050
## 315 316 317 318 319
## 0.5875763431 -0.4078496593 0.2353657459 0.3752687472 0.3007912347
## 320 321 322 323 324
## 0.0219233387 -0.5585097529 0.0920338782 0.4985910974 -0.2534512110
## 325 326 327 328 329
## -0.1352546575 -0.0338617618 -1.2401356127 -0.0603990799 0.6927204590
## 330 331 332 333 334
## 0.8101645216 0.4554625066 0.2758977507 -0.1558902425 0.2324918101
## 335 336 337 338 339
## -0.1571132546 -0.3554635846 0.1720243647 -0.0368614666 -0.2860883750
## 340 341 342 343 344
## 0.3664146703 0.3245726439 -0.8113220120 0.3094211668 0.1261280314
## 345 346 347 348 349
## 0.1013780624 0.5355813115 -0.2189059879 0.4203520863 0.4150589674
## 350 351 352 353 354
## 0.3031770151 0.1136186294 0.3525790847 0.0603945804 0.6853335007
## 355 356 357 358 359
## 0.3605603211 -0.5404365110 -0.6752436627 0.5970516429 0.8297212770
## 360 361 362 363 364
## 0.7278450588 0.5652834562 0.5630755331 -0.1175717912 -0.1903461945
## 365 366 367 368 369
## 0.0972404074 0.3422963065 0.3265283580 0.0821512567 0.4221394520
## 370 371 372 373 374
## 0.3144995798 0.0242426290 -0.0869549654 0.1292901847 0.0371106374
## 375 376 377 378 379
## 0.1510399797 0.1887376894 0.2498141128 -0.1476159290 -0.2584843004
## 380 381 382 383 384
## 0.2742931587 0.3827214873 0.2861100347 0.0320705553 -0.8687612922
## 385 386 387 388 389
## -0.6717371112 0.0901594979 0.3829023442 -0.0934348061 -0.0938720504
## 390 391 392 393 394
## 0.1243421596 0.0823670432 -0.4012690476 -0.3010281636 -0.0453070090
## 395 396 397 398 399
## -0.1682664417 -0.0227266962 -0.1872004916 -0.1452224339 -0.5144250145
## 400 401 402 403 404
## -0.1922387100 -0.0878008475 -0.0624489138 -0.2762842108 0.0024621932
## 405 406 407 408 409
## -0.0521510737 -0.7394339480 0.0295910486 -0.2974149703 -0.4524329524
## 410 411 412 413 414
## -0.0942575808 -0.2679268279 -0.1104944518 -0.5897524445 0.3438203257
## 415 416 417 418 419
## -0.1288860696 -0.2150139160 -0.0303903430 0.0037787687 -0.4397751792
## 420 421 422 423 424
## -0.6832706400 -0.4453951363 -0.1344499452 -0.8179229615 -0.4643839583
## 425 426 427 428 429
## 0.5094620775 -0.3647641012 0.3028159342 0.2062176388 0.1865326352
## 430 431 432 433 434
## -0.5719646627 0.1892242928 0.0735899417 -0.4111611070 0.2540204491
## 435 436 437 438 439
## 0.0494242221 -0.5904800236 -0.1388350201 -0.1684062474 -0.1357092483
## 440 441 442 443 444
## 0.1638572878 0.4641277285 0.9046284552 -0.5630378051 -0.2394969869
## 445 446 447 448 449
## -0.1976548938 -0.2692456496 0.0486816515 0.2693518653 0.1750217782
## 450 451 452 453 454
## -0.3212230719 -0.1564946816 -0.2735179742 -0.1829370659 -0.0562354176
## 455 456 457 458 459
## 0.2751055137 0.1558797044 0.1341932450 -0.3953978283 0.2066401363
## 460 461 462 463 464
## 0.6027321415 -0.6998549402 0.0009059039 -0.0013204327 0.0471160495
## 465 466 467 468 469
## 0.3756997387 0.7391826271 -0.3535968665 -0.1872812377 -0.4631693409
## 470 471 472 473 474
## -0.4225914438 0.2121285303 0.0406720251 -0.3903567773 -0.2813712050
## 475 476 477 478 479
## -0.5980437445 1.1517746897 -0.7341497203 0.2773720907 0.3208178831
## 480 481 482 483 484
## 0.3306062548 0.3199183622 0.5542635356 -0.8634054777 -0.1105232295
## 485 486 487 488 489
## 0.2386241573 -0.0339323640 0.1725353984 -0.1361991729 0.3281013347
## 490
## -0.0849704518
png(filename="ardl_92_forecast_acf.png", units="cm", res = 700,
width = 20,height = 15)
grid.arrange(mod_ardl92_acf,
mod_ardl92_meck_acf,
mod_ardl92_hanover_acf)
dev.off()
## quartz_off_screen
## 2
#ARDL forecasting plots
full_cases_wastewater_weather_data_test <-
cbind(full_cases_wastewater_weather_data_test,f_ardl92$forecasts[,2],
f_ardl92$forecasts[,1],f_ardl92$forecasts[,3],
f_ardl914_weather$forecasts[,2],f_ardl914_weather$forecasts[,1],
f_ardl914_weather$forecasts[,3])
full_cases_wastewater_weather_data_meck_test <-
cbind(full_cases_wastewater_weather_data_meck_test,f_ardl92_meck$forecasts[,2],
f_ardl92_meck$forecasts[,1],f_ardl92_meck$forecasts[,3],
f_ardl914_weather_meck$forecasts[,2],f_ardl914_weather_meck$forecasts[,1],
f_ardl914_weather_meck$forecasts[,3])
full_cases_wastewater_weather_data_hanover_test <-
cbind(full_cases_wastewater_weather_data_hanover_test,f_ardl92_hanover$forecasts[,2],
f_ardl92_hanover$forecasts[,1],f_ardl92_hanover$forecasts[,3],
f_ardl914_weather_hanover$forecasts[,2],f_ardl914_weather_hanover$forecasts[,1],
f_ardl914_weather_hanover$forecasts[,3])
wake_ardl_noweather_plot <-
full_cases_wastewater_weather_data_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_test, aes(ymin = f_ardl92$forecasts[,1], ymax = f_ardl92$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,f_ardl92$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
meck_ardl_noweather_plot <- full_cases_wastewater_weather_data_meck_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_meck_test, aes(ymin = f_ardl92_meck$forecasts[,1], ymax = f_ardl92_meck$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,f_ardl92_meck$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
hanover_ardl_noweather_plot <- full_cases_wastewater_weather_data_hanover_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_hanover_test, aes(ymin = f_ardl92_hanover$forecasts[,1], ymax = f_ardl92_hanover$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,f_ardl92_hanover$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "bottom") + ylab("")
wake_ardl_weather_plot <-
full_cases_wastewater_weather_data_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_test, aes(ymin = f_ardl914_weather$forecasts[,1], ymax = f_ardl914_weather$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,f_ardl914_weather$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
meck_ardl_weather_plot <- full_cases_wastewater_weather_data_meck_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_meck_test, aes(ymin = f_ardl914_weather_meck$forecasts[,1], ymax = f_ardl914_weather_meck$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,f_ardl914_weather_meck$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
hanover_ardl_weather_plot <- full_cases_wastewater_weather_data_hanover_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_hanover_test, aes(ymin = f_ardl914_weather_hanover$forecasts[,1], ymax = f_ardl914_weather_hanover$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,f_ardl914_weather_hanover$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "bottom") + ylab("")
png(filename = "ardl_plots.png", res = 700, units = "cm",
width = 20, height = 15)
grid.arrange(wake_ardl_noweather_plot,
wake_ardl_weather_plot,
meck_ardl_noweather_plot,
meck_ardl_weather_plot,
hanover_ardl_noweather_plot,
hanover_ardl_weather_plot,
ncol=2,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
Distributed Lag Model
#wastewater only#
#wake
lowest_rmse_dl_wake <- Inf
best_mod_dl_wake <- NULL
for (q in seq(1,6)){
mod <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_test[,7]),h=14,
interval = TRUE)
forecast_acc <- rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f$forecasts[,2]) #interchanged between RMSE and MAE
if (forecast_acc<lowest_rmse_dl_wake){
lowest_rmse_dl_wake<- forecast_acc
best_mod_dl_wake <-mod
}
}
lowest_rmse_dl_wake
## [1] 0.2338659
summary(best_mod_dl_wake) #DL(13) (lowest RMSE), DL(14) (lowest MAE)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.69819 -0.33444 0.00444 0.30269 1.62613
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.84578 0.23889 -32.843 < 2e-16 ***
## log_viral_gene.t 0.16035 0.04296 3.732 0.000213 ***
## log_viral_gene.1 0.05599 0.05482 1.021 0.307572
## log_viral_gene.2 0.02580 0.05472 0.472 0.637475
## log_viral_gene.3 0.06471 0.05463 1.185 0.236797
## log_viral_gene.4 0.05959 0.05473 1.089 0.276826
## log_viral_gene.5 0.07734 0.05482 1.411 0.158935
## log_viral_gene.6 0.12980 0.04294 3.023 0.002641 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.575 on 476 degrees of freedom
## Multiple R-squared: 0.7365, Adjusted R-squared: 0.7326
## F-statistic: 190 on 7 and 476 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 847.8488 885.4875
mod_dl13 <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,q=13)
f_dl13 <- forecast(mod_dl13, x= t(full_cases_wastewater_weather_data_test[,7]),h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl13$forecasts)
## [1] 0.2065803
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl13$forecasts)
## [1] 0.1775717
checkresiduals(mod_dl13)
## 1 2 3 4 5
## 0.0095287990 -0.1190625530 -0.1531323134 0.0030576620 0.0136981667
## 6 7 8 9 10
## -0.0261142391 0.1216989061 0.0220785102 -0.1605813445 0.1785185379
## 11 12 13 14 15
## 0.0002528995 -0.0050411761 -0.2673081646 0.3675934026 0.0258890742
## 16 17 18 19 20
## -0.2323555239 0.2171339457 0.0204643421 0.1531779335 0.2517727997
## 21 22 23 24 25
## 0.2159750800 -0.0664740493 -0.3059228352 0.0611127354 -0.1030060694
## 26 27 28 29 30
## -0.0544013296 0.0469333906 -0.0452826992 -0.3949227979 -0.3531188592
## 31 32 33 34 35
## -0.3844135914 -0.1717731253 -0.1677140667 -0.3300973093 -0.0682872428
## 36 37 38 39 40
## -0.3310753380 -0.0652631266 -0.2047202392 -0.1949149682 -0.5059344021
## 41 42 43 44 45
## -0.3708936641 -0.1784788716 -0.1033662599 0.0841552031 -0.0395917719
## 46 47 48 49 50
## -0.0169014316 0.2738984334 0.4509111559 0.2785006235 0.4159804611
## 51 52 53 54 55
## 0.4353278508 0.5811283983 0.2265580547 0.2605957587 0.4874291118
## 56 57 58 59 60
## 0.3766836448 0.5413251636 0.7822674443 0.6113341442 0.6320182852
## 61 62 63 64 65
## 0.7296493097 0.3198245558 0.2729219371 0.1208551791 0.3032733150
## 66 67 68 69 70
## 0.1454792749 0.0131425149 -0.3144898677 -0.1486766130 -0.2703568530
## 71 72 73 74 75
## -0.0804399997 0.2007612103 -0.2139454569 0.0276957708 0.2806133265
## 76 77 78 79 80
## -0.1860228653 -0.4627968558 -0.2250485083 0.4136338815 0.6928904691
## 81 82 83 84 85
## 0.3338986126 0.2337289713 0.4859215444 0.4717119703 0.5376593731
## 86 87 88 89 90
## 0.7550474789 0.2957337293 0.4997706712 0.2387781890 0.2288796703
## 91 92 93 94 95
## 0.1762464834 0.1679184147 0.1950958591 0.1322861845 0.0056351663
## 96 97 98 99 100
## 0.0670879172 0.2018038871 0.2374408930 0.4707799263 0.6366294000
## 101 102 103 104 105
## 0.4636423640 0.4286462584 0.4379097308 0.3039290953 0.3858051744
## 106 107 108 109 110
## 0.1003972658 0.5755059767 0.1601121259 0.4278458633 0.2731736870
## 111 112 113 114 115
## 0.4419345923 0.6058745326 0.6577245491 0.8391310786 0.7369989000
## 116 117 118 119 120
## 0.9121247045 1.0834389217 0.8331868785 0.9874412281 0.8447164736
## 121 122 123 124 125
## 0.9935330582 0.9242205485 1.3084602577 0.9249033331 1.1805858542
## 126 127 128 129 130
## 0.6291488043 0.8845576624 1.0980101780 0.7036880288 0.9551474913
## 131 132 133 134 135
## 0.3246270113 0.2293898636 0.1702282967 0.2633715547 0.5195783778
## 136 137 138 139 140
## -1.0115844170 -0.3440971699 -1.4611202944 -0.5718723079 -0.0620514067
## 141 142 143 144 145
## 0.0502913088 0.3064782031 -0.5756364792 -0.7102525549 -0.5304807023
## 146 147 148 149 150
## -0.4409715142 -0.8216946599 -0.4266274817 -0.5141425949 -0.1281811336
## 151 152 153 154 155
## -0.2199366064 0.0627077707 -0.0356243330 0.1666909875 0.0037317645
## 156 157 158 159 160
## -0.2279486654 -0.4890579931 -0.2104378956 -0.9660052668 -0.5753503615
## 161 162 163 164 165
## -0.8435821343 -0.3407053536 -0.5285139637 -0.6205813727 -0.8762931537
## 166 167 168 169 170
## -0.9108998398 -0.6876315959 -0.5732927156 -0.8549777045 -2.5464660238
## 171 172 173 174 175
## -1.0196630431 -0.8949945460 -0.8511860569 -0.8429210867 -0.2374671489
## 176 177 178 179 180
## -0.3235065113 -0.1816112110 -0.1531358286 -0.2200797775 -0.5831020965
## 181 182 183 184 185
## 0.1307713552 -0.1006437630 -0.1083236903 0.1756074281 0.0444798527
## 186 187 188 189 190
## 0.3319336510 0.0239481241 0.3824724153 0.2569514516 0.2636273526
## 191 192 193 194 195
## 0.6315405112 0.3695888959 0.2119642917 0.1919769638 0.5138237890
## 196 197 198 199 200
## 0.4138427721 0.2867494814 0.2155279390 0.2274736345 0.0796518050
## 201 202 203 204 205
## 0.1060026017 0.3204923720 0.0404962344 0.0853213427 0.2438579779
## 206 207 208 209 210
## 0.1779288594 0.0891377187 0.0432960360 0.3103792736 0.2281222043
## 211 212 213 214 215
## 0.1236221727 0.1633486763 0.3235666022 0.1623906273 0.2740916076
## 216 217 218 219 220
## 0.5086362607 0.4734036100 0.5117131059 0.3616221789 0.6917956274
## 221 222 223 224 225
## 0.4847251927 0.6232416418 0.6375417112 0.6673949254 1.1145787086
## 226 227 228 229 230
## 0.3862205725 0.4981110260 0.4098025871 0.7143797946 0.5379146444
## 231 232 233 234 235
## 0.2979850152 0.2021777012 -0.5105105560 -1.9138958805 -0.1518195302
## 236 237 238 239 240
## -0.4888675546 -0.5724222352 -0.2815968060 -0.2388632759 -0.5393945041
## 241 242 243 244 245
## -0.3535085946 -0.5945209252 -0.5220520655 -0.4873440989 -0.5401129543
## 246 247 248 249 250
## -0.4065617273 -0.6664851319 -0.4767989824 -0.5352771914 -0.5779643305
## 251 252 253 254 255
## -0.5839324467 -0.4201575631 -0.6731663205 -0.9992006269 -0.3664053529
## 256 257 258 259 260
## -0.5702757214 -0.5596094756 -0.5228722667 -0.5166083808 -0.2655802573
## 261 262 263 264 265
## -0.7856158601 -0.6169771715 -0.7049805934 -0.5114925608 -0.5309703411
## 266 267 268 269 270
## 0.2399412232 -0.6051581838 -0.0059002330 -0.3519376422 -0.2098972172
## 271 272 273 274 275
## 0.3251098584 0.0843993710 -0.3616465191 -0.5206821393 -1.0270082658
## 276 277 278 279 280
## -0.1735646731 -0.2792434012 -0.1305361500 -2.6052706205 -1.8889804041
## 281 282 283 284 285
## 0.1418332207 -0.6009130439 -0.4010935176 -0.0173228884 -0.0505879051
## 286 287 288 289 290
## -0.2107403372 -0.0475383556 0.0022695219 -0.5074790956 -0.3666193633
## 291 292 293 294 295
## -0.4222073272 -0.2772176786 -0.6213116978 -0.3665745526 -0.3876669866
## 296 297 298 299 300
## -0.0774512187 -0.4288776958 -1.3795654658 -0.3263101456 -0.7524327828
## 301 302 303 304 305
## -0.0954234622 -0.4930710780 -0.2300179742 -0.1211002886 -0.3669266877
## 306 307 308 309 310
## -0.0209295706 0.3341295772 0.5192608572 0.9367138810 0.7860341469
## 311 312 313 314 315
## 0.4019857183 0.1918182390 0.1456186230 -0.3586969576 0.1490635550
## 316 317 318 319 320
## 0.4551800817 0.2145735941 0.5818535232 0.4892598622 0.9696658384
## 321 322 323 324 325
## 0.6913460519 0.6709268713 0.6574151102 0.5882864085 0.2908777784
## 326 327 328 329 330
## 0.3001517618 0.2613459076 -0.1673239970 0.1462799103 0.0363008613
## 331 332 333 334 335
## 0.1662487167 0.0390800932 -0.2331726209 -0.1887791856 -0.1968449440
## 336 337 338 339 340
## -0.0382003496 0.2897354781 0.1771268222 0.0940023131 0.3214349057
## 341 342 343 344 345
## 0.5002719619 0.8752746390 0.2933871629 -0.1518127057 1.0294021204
## 346 347 348 349 350
## 1.3974973867 1.5729908779 1.4411227746 1.4552885784 0.9695554381
## 351 352 353 354 355
## 1.0479506098 1.1558670944 1.3524316054 1.7058411420 1.4460780938
## 356 357 358 359 360
## 1.3356012519 1.1927786580 1.1324214981 0.4611187124 1.1398864008
## 361 362 363 364 365
## 0.8741525251 0.9965355980 0.6499429477 0.5565711610 0.2440844197
## 366 367 368 369 370
## -1.1228020026 -0.2715076753 0.6729899101 0.5860328439 0.4523365155
## 371 372 373 374 375
## -0.7845298391 -1.3073478210 -0.0740773196 0.5996424827 -0.0105626928
## 376 377 378 379 380
## -0.1102625504 -0.1950236588 -0.1132130882 -0.6834201037 -0.3669367429
## 381 382 383 384 385
## 0.4060755398 0.0549523976 -0.1450415496 -0.1118276624 0.1533060313
## 386 387 388 389 390
## 0.1062347387 0.2103637031 -0.1768461765 -0.0475146478 0.0853599094
## 391 392 393 394 395
## -0.2918135507 -0.3436818194 -0.2111585341 -0.0927968058 0.0417605779
## 396 397 398 399 400
## -0.2566887382 -0.2884695620 -0.1111722614 -0.3261228158 -0.4511201333
## 401 402 403 404 405
## -0.1144284548 -0.2773431750 -0.4230133363 -0.5846508273 -0.5429144957
## 406 407 408 409 410
## -0.3734626251 -0.9119074676 -0.4330448605 -0.7825021808 -0.7461967081
## 411 412 413 414 415
## -0.5831842032 0.0182994108 -0.6625402759 -0.3779988072 -0.0144497165
## 416 417 418 419 420
## -0.2531398401 -0.0966306430 -0.6382839044 0.0899330845 -0.3272473122
## 421 422 423 424 425
## -0.1910606065 -0.3627512827 -0.0012667909 -0.6182901022 -0.0532455764
## 426 427 428 429 430
## -0.1194188918 -0.4184490421 -0.3958815610 -0.1594862729 -0.1253070859
## 431 432 433 434 435
## -0.5417898680 -0.3883179832 -0.1820047742 -0.4609395941 -0.7754988071
## 436 437 438 439 440
## -0.7215218919 -0.9246462748 -0.3817860348 -0.7616585272 -0.6119288683
## 441 442 443 444 445
## -0.1375220001 -0.4939069036 -0.2968563304 -0.2997388041 -0.7178070830
## 446 447 448 449 450
## -0.2858385631 -0.4554618725 -0.2932202790 -0.0579412888 -0.2642574159
## 451 452 453 454 455
## -0.3665627261 -0.0332858150 0.1010816629 0.1257325527 -0.0526402066
## 456 457 458 459 460
## 0.2793252192 0.0895443023 -0.0916205798 0.0760989617 -0.1942204355
## 461 462 463 464 465
## -0.0607358875 0.0233958328 0.0412930454 0.2597501084 -0.2567437918
## 466 467 468 469 470
## -0.1226501142 -0.0914894524 -0.3034338374 -0.1470025648 -0.1449935697
## 471 472 473 474 475
## -0.4445127463 -0.2204801961 -0.2360937957 -0.1420129309 0.0683415345
## 476 477
## -0.1160366572 0.1825599262
mod_dl14 <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,q=14)
summary(mod_dl14)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.60667 -0.34908 -0.02616 0.31306 1.71001
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.264570 0.243490 -33.942 < 2e-16 ***
## log_viral_gene.t 0.167381 0.042160 3.970 8.33e-05 ***
## log_viral_gene.1 0.044522 0.054177 0.822 0.4116
## log_viral_gene.2 -0.001578 0.054376 -0.029 0.9769
## log_viral_gene.3 0.046533 0.054394 0.855 0.3927
## log_viral_gene.4 0.043612 0.054553 0.799 0.4245
## log_viral_gene.5 0.075028 0.054689 1.372 0.1708
## log_viral_gene.6 0.049399 0.054840 0.901 0.3682
## log_viral_gene.7 -0.025818 0.054896 -0.470 0.6384
## log_viral_gene.8 0.002526 0.054849 0.046 0.9633
## log_viral_gene.9 0.034643 0.054680 0.634 0.5267
## log_viral_gene.10 0.032270 0.054533 0.592 0.5543
## log_viral_gene.11 0.081860 0.054385 1.505 0.1330
## log_viral_gene.12 -0.029197 0.054393 -0.537 0.5917
## log_viral_gene.13 0.003275 0.054290 0.060 0.9519
## log_viral_gene.14 0.076729 0.042232 1.817 0.0699 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5582 on 460 degrees of freedom
## Multiple R-squared: 0.7561, Adjusted R-squared: 0.7481
## F-statistic: 95.07 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 813.5694 884.3815
f_dl14 <- forecast(mod_dl14, x= t(full_cases_wastewater_weather_data_test[,7]),
h=14, interval = TRUE)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl14$forecasts[,2])
## [1] 0.214038
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl14$forecasts[,2])
## [1] 0.1774498
checkresiduals(mod_dl14)
## 1 2 3 4 5 6
## -0.151770801 -0.160174319 -0.006891305 0.012071577 -0.068008232 0.122592200
## 7 8 9 10 11 12
## 0.015847908 -0.178071430 0.214099747 -0.006353717 -0.012215233 -0.298606308
## 13 14 15 16 17 18
## 0.354637808 0.025646543 -0.260584528 0.180020051 0.013853802 0.158328818
## 19 20 21 22 23 24
## 0.278353673 0.210017083 -0.078877295 -0.348110739 0.055222675 -0.110048519
## 25 26 27 28 29 30
## -0.061257221 -0.044888949 -0.037927120 -0.391780768 -0.357219577 -0.325654025
## 31 32 33 34 35 36
## -0.173423164 -0.161965045 -0.331116892 -0.070850976 -0.327220624 -0.077795680
## 37 38 39 40 41 42
## -0.192371480 -0.199630447 -0.499721719 -0.339997397 -0.186092416 -0.112659390
## 43 44 45 46 47 48
## 0.046153616 -0.065795631 -0.027007380 0.272730134 0.385322871 0.284586325
## 49 50 51 52 53 54
## 0.408328451 0.418240641 0.607870058 0.227049609 0.244602361 0.437649300
## 55 56 57 58 59 60
## 0.361156912 0.546368097 0.755777260 0.480700608 0.637950909 0.761534885
## 61 62 63 64 65 66
## 0.367490147 0.299815161 0.125096013 0.327222264 0.264879971 0.021003598
## 67 68 69 70 71 72
## -0.314816009 -0.158956628 -0.277862458 -0.061712910 0.215764953 -0.300915457
## 73 74 75 76 77 78
## 0.034125718 0.320742606 -0.013196360 -0.464188949 -0.230510455 0.398974451
## 79 80 81 82 83 84
## 0.678452605 0.333376179 0.221424191 0.490438548 0.447209701 0.534268079
## 85 86 87 88 89 90
## 0.709815225 0.119640883 0.504932076 0.261929540 0.246888146 0.194527175
## 91 92 93 94 95 96
## 0.178860328 0.206730858 0.252978892 0.005364263 0.074426266 0.216287910
## 97 98 99 100 101 102
## 0.232817539 0.472290377 0.614895530 0.447324577 0.424654756 0.445229243
## 103 104 105 106 107 108
## 0.310757531 0.385827965 0.093229086 0.539775588 0.138891230 0.432588068
## 109 110 111 112 113 114
## 0.280276822 0.381751416 0.606126225 0.676981509 0.861906417 0.755161556
## 115 116 117 118 119 120
## 0.905947690 1.096363380 0.879085200 0.986306869 0.824226121 0.934572457
## 121 122 123 124 125 126
## 0.910965863 1.303534614 0.903807919 0.996189016 0.642240600 0.893461200
## 127 128 129 130 131 132
## 1.098934200 0.717405303 0.966141121 0.347449470 0.226289563 0.190708147
## 133 134 135 136 137 138
## 0.279640583 0.546293239 -0.972154654 -0.343724632 -1.439011674 -0.468140737
## 139 140 141 142 143 144
## -0.038232381 0.061734132 0.289038977 -0.648272094 -0.593070505 -0.507174123
## 145 146 147 148 149 150
## -0.433670957 -0.830026838 -0.441469781 -0.549782252 -0.114253460 -0.211018737
## 151 152 153 154 155 156
## -0.002542970 -0.025310874 0.152103161 0.021355744 -0.153498703 -0.488846098
## 157 158 159 160 161 162
## -0.292301718 -0.917386352 -0.565715895 -0.853973793 -0.323561354 -0.431294276
## 163 164 165 166 167 168
## -0.624386866 -0.973825825 -0.870499160 -0.656768083 -0.559515570 -0.817463012
## 169 170 171 172 173 174
## -2.439120965 -1.011462182 -0.885873005 -0.813675933 -0.818385289 -0.226150827
## 175 176 177 178 179 180
## -0.307792930 -0.183935955 -0.076929703 -0.215211957 -0.557805408 0.148763847
## 181 182 183 184 185 186
## -0.101680887 -0.117617739 0.143736499 0.020394433 0.337207754 0.045956078
## 187 188 189 190 191 192
## 0.332593271 0.256071911 0.247573241 0.629550849 0.509287247 0.192702377
## 193 194 195 196 197 198
## 0.071292443 0.565404648 0.436179259 0.301658228 0.232234299 0.393091647
## 199 200 201 202 203 204
## 0.079781736 0.118662310 0.338854035 0.045047977 0.088193667 0.237000094
## 205 206 207 208 209 210
## 0.238516762 0.086160984 0.041897754 0.315808665 0.229016112 0.125181519
## 211 212 213 214 215 216
## 0.151657938 0.337117793 0.162295906 0.296032161 0.514344361 0.468765657
## 217 218 219 220 221 222
## 0.496941398 0.346308667 0.712701681 0.474850754 0.594063627 0.649302975
## 223 224 225 226 227 228
## 0.655152141 1.093468567 0.364177085 0.531892550 0.388969558 0.627855968
## 229 230 231 232 233 234
## 0.558245460 0.300468018 0.212893475 -0.522911391 -1.841610748 -0.155285556
## 235 236 237 238 239 240
## -0.508681021 -0.579301985 -0.268928725 -0.189132236 -0.548010627 -0.388553086
## 241 242 243 244 245 246
## -0.570005532 -0.318321249 -0.476077039 -0.551777154 -0.429298466 -0.723291715
## 247 248 249 250 251 252
## -0.497671782 -0.548269407 -0.597052392 -0.719545452 -0.418849460 -0.672944848
## 253 254 255 256 257 258
## -1.010622705 -0.327623496 -0.575844083 -0.556350035 -0.523688877 -0.519657389
## 259 260 261 262 263 264
## -0.268375536 -0.803853303 -0.610959894 -0.710925756 -0.510139753 -0.539475414
## 265 266 267 268 269 270
## 0.234843138 -0.608050746 -0.027640151 -0.374300241 -0.212675738 0.334159885
## 271 272 273 274 275 276
## 0.076729409 -0.369232372 -0.523525111 -1.050303551 -0.205229336 -0.283065176
## 277 278 279 280 281 282
## -0.125127059 -2.606668860 -1.887651121 0.137770559 -0.614603483 -0.393221520
## 283 284 285 286 287 288
## -0.027077421 -0.031360472 -0.227814319 -0.047417728 -0.020386512 -0.539459137
## 289 290 291 292 293 294
## -0.383600678 -0.422027824 -0.323895183 -0.631557439 -0.365336871 -0.369111965
## 295 296 297 298 299 300
## -0.035236118 -0.547808614 -1.315971321 -0.329583472 -0.750814942 -0.091505927
## 301 302 303 304 305 306
## -0.482518346 -0.259376639 -0.122673196 -0.359898283 0.033848038 0.335394645
## 307 308 309 310 311 312
## 0.524354738 0.927982380 0.780829953 0.418791558 0.186413545 0.182083536
## 313 314 315 316 317 318
## -0.373833890 0.127315760 0.390806471 0.138672724 0.573963506 0.458075879
## 319 320 321 322 323 324
## 0.839090143 0.739579581 0.686325113 0.675773388 0.831578480 0.341718760
## 325 326 327 328 329 330
## 0.290288367 0.168494837 -0.144210596 0.144610634 0.048771048 0.254732871
## 331 332 333 334 335 336
## 0.042042209 -0.225549990 -0.236827529 -0.176274543 -0.038612283 0.312138062
## 337 338 339 340 341 342
## 0.238171523 0.136415396 0.276010470 0.540565247 0.882857955 0.296840260
## 343 344 345 346 347 348
## -0.137283545 1.023863671 1.419062128 1.570806375 1.494699904 1.448212011
## 349 350 351 352 353 354
## 0.970092989 1.044901228 1.096022120 1.360122567 1.710005296 1.493208650
## 355 356 357 358 359 360
## 1.339123639 1.201445618 1.143456231 0.512135705 1.140535149 0.884675146
## 361 362 363 364 365 366
## 1.011324742 0.652221238 0.549047199 0.263673674 -1.126485235 -0.316701781
## 367 368 369 370 371 372
## 0.717132716 0.585472735 0.438581794 -0.771989008 -1.290460799 -0.108444124
## 373 374 375 376 377 378
## 0.646418665 -0.028111462 0.033091842 -0.250391953 -0.174030337 -0.676824629
## 379 380 381 382 383 384
## -0.411439361 0.179887039 0.042274760 -0.135621401 -0.035189170 0.120473964
## 385 386 387 388 389 390
## 0.082071971 0.127908668 -0.062952369 -0.241917541 0.150867958 -0.306590869
## 391 392 393 394 395 396
## -0.351989173 -0.248284189 -0.229355365 0.066177156 -0.236726148 -0.360486102
## 397 398 399 400 401 402
## -0.117368445 -0.335625206 -0.432859367 -0.091015252 -0.352087825 -0.416276302
## 403 404 405 406 407 408
## -0.549777331 -0.545873481 -0.383512457 -0.921388416 -0.504774156 -0.748695127
## 409 410 411 412 413 414
## -0.782727437 -0.560935127 -0.008560035 -0.664322358 -0.408533211 -0.069387305
## 415 416 417 418 419 420
## -0.273464059 -0.132595114 -0.594053109 0.066738616 -0.340858730 -0.257368374
## 421 422 423 424 425 426
## -0.414811767 -0.060867515 -0.585942332 -0.240590621 -0.088740505 -0.410675912
## 427 428 429 430 431 432
## -0.374591384 0.066396452 -0.154500894 -0.535570467 -0.453401557 -0.172807709
## 433 434 435 436 437 438
## -0.458378403 -0.781191169 -0.629485851 -0.904539340 -0.437470823 -0.822157694
## 439 440 441 442 443 444
## -0.606324690 -0.105332875 -0.463414756 -0.232166849 -0.367055143 -0.600122567
## 445 446 447 448 449 450
## -0.257259980 -0.453475603 -0.286459956 -0.056093756 -0.301833108 -0.395416052
## 451 452 453 454 455 456
## 0.025042902 0.097045855 0.140881259 -0.036051822 0.280518057 0.096068539
## 457 458 459 460 461 462
## -0.029904984 0.081309895 -0.180521132 -0.067073493 0.033031739 0.025108241
## 463 464 465 466 467 468
## 0.216817157 -0.279499964 -0.066774088 -0.114070837 -0.288768122 -0.131827100
## 469 470 471 472 473 474
## -0.147972310 -0.398907266 -0.195345702 -0.192634128 -0.193318660 0.072075552
## 475 476
## -0.107907378 0.190390635
exp(f_dl14$forecasts[1,2])
## [1] 5.260291
exp(f_dl14$forecasts[1,1])
## [1] 1.989456
exp(f_dl14$forecasts[1,3])
## [1] 18.21049
exp(f_dl14$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_test[1,6])
## [1] -3.457252
exp(f_dl14$forecasts[7,2])
## [1] 6.063562
exp(f_dl14$forecasts[7,1])
## [1] 2.076791
exp(f_dl14$forecasts[7,3])
## [1] 17.46885
exp(f_dl14$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_test[7,6])
## [1] -0.93469
exp(f_dl14$forecasts[14,2])
## [1] 7.755135
exp(f_dl14$forecasts[14,1])
## [1] 2.46803
exp(f_dl14$forecasts[14,3])
## [1] 23.62644
exp(f_dl14$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_test[14,6])
## [1] 2.048415
mod_dl2 <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_train,q=2)
summary(mod_dl2)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.97051 -0.36680 0.00761 0.33854 2.00663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.25687 0.25070 -28.946 < 2e-16 ***
## log_viral_gene.t 0.23468 0.04507 5.207 2.84e-07 ***
## log_viral_gene.1 0.06274 0.05888 1.066 0.287
## log_viral_gene.2 0.23742 0.04503 5.272 2.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6274 on 484 degrees of freedom
## Multiple R-squared: 0.6849, Adjusted R-squared: 0.683
## F-statistic: 350.7 on 3 and 484 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 935.9223 956.8739
f_dl2 <- forecast(mod_dl2, x= t(full_cases_wastewater_weather_data_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl2$forecasts)
## [1] 0.2567277
mae(full_cases_wastewater_weather_data_test$log_mean_new_cases,
f_dl2$forecasts)
## [1] 0.218327
tsdisplay(residuals(mod_dl2))
## 1 2 3 4 5 6
## 0.270051697 0.392966818 0.476158009 0.415748845 0.197135746 0.465756643
## 7 8 9 10 11 12
## 0.365134193 0.328436588 0.306786218 0.177672422 0.184030101 0.098566110
## 13 14 15 16 17 18
## 0.005867637 0.016270849 0.147498017 0.240383389 0.261905728 0.363702876
## 19 20 21 22 23 24
## 0.226906066 -0.077599345 0.316299046 0.135240553 0.207163908 -0.155827697
## 25 26 27 28 29 30
## 0.533140410 0.151397722 0.224921420 0.637884213 0.340086219 0.423503431
## 31 32 33 34 35 36
## 0.270500263 0.263643865 -0.025319008 -0.304885931 0.118496716 -0.159767758
## 37 38 39 40 41 42
## -0.004742163 -0.005640049 -0.132666288 -0.471258345 -0.555719617 -0.474181580
## 43 44 45 46 47 48
## -0.217437108 -0.110281259 -0.226478926 0.047789391 -0.240644912 0.202136736
## 49 50 51 52 53 54
## 0.073357057 0.068854350 -0.249763608 -0.215012896 -0.013302435 0.009360923
## 55 56 57 58 59 60
## 0.225891547 0.106107121 0.163011009 0.559176026 1.043331103 0.761606541
## 61 62 63 64 65 66
## 0.777353232 0.556032834 0.692369147 0.278467615 0.362457109 0.153941130
## 67 68 69 70 71 72
## -0.004039909 0.050538650 0.305321606 0.150670059 0.303042245 0.546206241
## 73 74 75 76 77 78
## 0.566199603 0.286710216 0.069891428 -0.481931840 -0.457480874 -0.363173383
## 79 80 81 82 83 84
## -0.455174495 -0.138861306 -0.421072140 -0.398024698 -0.154741923 -0.568782034
## 85 86 87 88 89 90
## 0.051396780 0.404503603 0.593229646 0.187685904 0.246293664 0.768840503
## 91 92 93 94 95 96
## 0.971739397 0.595583462 0.487198307 0.295263209 0.247191601 0.167818512
## 97 98 99 100 101 102
## 0.441929575 -0.050102151 0.159044587 0.012565488 0.113200502 0.044458342
## 103 104 105 106 107 108
## 0.091547047 0.042663336 0.113370311 0.037418062 0.167752143 0.329398388
## 109 110 111 112 113 114
## 0.377656898 0.553616015 0.898230235 0.669288126 0.589568706 0.482455191
## 115 116 117 118 119 120
## 0.278051727 0.349376460 0.027104377 0.397545451 -0.003786059 0.218715987
## 121 122 123 124 125 126
## 0.194446749 0.285878695 0.623632752 0.691485547 1.494795373 1.345427854
## 127 128 129 130 131 132
## 1.419388080 1.470312443 1.087359303 1.259729105 1.055021747 1.064779239
## 133 134 135 136 137 138
## 0.988724252 1.182006885 0.920494249 0.963690759 0.294742460 0.485437719
## 139 140 141 142 143 144
## 0.345489879 0.060806845 0.476635035 -0.049984952 0.160325418 -0.355520786
## 145 146 147 148 149 150
## -0.287642492 -0.020865928 -1.418223137 -0.550539502 -1.666149567 -0.678315446
## 151 152 153 154 155 156
## -0.130523792 0.200301142 0.514793178 -0.591599357 -0.750730105 -0.778953428
## 157 158 159 160 161 162
## -0.616725269 -0.624296040 -0.287427807 -0.449411914 -0.349569682 -0.491121589
## 163 164 165 166 167 168
## -0.409269675 -0.432584269 0.232313580 0.021988546 -0.273046069 -0.691193476
## 169 170 171 172 173 174
## -0.587789326 -1.524106476 -1.110829482 -1.287740886 -0.841628967 -1.000483182
## 175 176 177 178 179 180
## -1.022017330 -1.395151934 -1.302321336 -1.299590451 -1.069169379 -1.425359426
## 181 182 183 184 185 186
## -2.970508001 -1.324335329 -1.193829999 -1.042744001 -1.042986365 -0.357452952
## 187 188 189 190 191 192
## -0.374422873 0.038573643 0.139257128 -0.121674589 -0.536092697 -0.255566064
## 193 194 195 196 197 198
## -0.365745394 0.139626215 0.401815614 0.278745047 0.156316024 -0.165588212
## 199 200 201 202 203 204
## -0.313004304 -0.354086961 -0.207277703 0.202083575 0.062430764 -0.135871772
## 205 206 207 208 209 210
## -0.209746572 -0.003618880 -0.050244154 0.005435248 -0.085656864 0.145511342
## 211 212 213 214 215 216
## -0.026051798 0.070372763 0.226212897 -0.060794842 -0.023578114 0.110740594
## 217 218 219 220 221 222
## 0.154817354 0.057539365 0.077035923 0.261975619 0.186807488 0.226747491
## 223 224 225 226 227 228
## 0.241652912 0.462981501 0.222490894 0.381470345 0.568158687 0.557901698
## 229 230 231 232 233 234
## 0.895083680 0.680714438 0.998050609 0.661825738 0.765809943 0.622840918
## 235 236 237 238 239 240
## 0.651075849 1.077073831 0.332076338 0.459665677 0.437390480 0.749655186
## 241 242 243 244 245 246
## 0.549148519 0.210065909 -0.527997274 -1.221193801 -2.422708327 -0.450573917
## 247 248 249 250 251 252
## -0.610231048 -0.810124779 -0.410089833 -0.294943033 -0.104015337 0.215190791
## 253 254 255 256 257 258
## -0.197778700 -0.025612119 -0.220297484 -0.248057534 -0.146142645 -0.481908547
## 259 260 261 262 263 264
## -0.263836756 -0.468252405 -0.397555413 -0.549355059 -0.402858334 -0.662335034
## 265 266 267 268 269 270
## -1.023264211 -0.306699790 -0.476700972 -0.385776165 -0.307324128 -0.346582205
## 271 272 273 274 275 276
## -0.178964351 -0.747413067 -0.534665919 -0.569661437 -0.291709850 -0.258698643
## 277 278 279 280 281 282
## 0.458341603 -0.468685588 0.080495990 -0.249485727 -0.095336840 0.513537199
## 283 284 285 286 287 288
## 0.208293724 -0.277121510 -0.521821984 -1.042768919 -0.165823650 -0.230022553
## 289 290 291 292 293 294
## -0.005820125 -2.367461701 -1.709146529 0.440407142 -0.384529244 -0.240862362
## 295 296 297 298 299 300
## 0.206936085 -0.039865951 0.206531557 0.105202687 0.071631134 -0.509327943
## 301 302 303 304 305 306
## -0.422332798 -0.355607411 -0.111628639 -0.564440837 -0.290865502 -0.659051495
## 307 308 309 310 311 312
## -0.204004155 -0.613664115 -1.470805973 -0.337429022 -0.867471546 -0.248035290
## 313 314 315 316 317 318
## -0.649431820 -0.403257322 -0.184479290 -0.437246758 0.085518248 0.610152696
## 319 320 321 322 323 324
## 0.914942979 2.006628712 1.675226452 0.947022561 0.383144247 -0.574389567
## 325 326 327 328 329 330
## -0.961788695 -0.298681841 0.545110400 0.293846282 0.257424952 0.071789745
## 331 332 333 334 335 336
## 0.129096393 0.075839849 0.374635320 0.563532411 0.680596171 0.213420359
## 337 338 339 340 341 342
## 0.160522090 -0.077909402 -0.613335222 -0.001095000 -0.278531529 -0.017642249
## 343 344 345 346 347 348
## -0.178417829 -0.420773912 -0.291468919 -0.401117168 -0.219447323 -0.064118479
## 349 350 351 352 353 354
## -0.151559737 -0.012681382 0.229603534 0.665857221 0.952500469 0.322748254
## 355 356 357 358 359 360
## -0.226422194 0.934061962 1.389460730 1.560308073 1.313311072 1.309050418
## 361 362 363 364 365 366
## 0.747963580 0.819291582 0.929753311 1.188165087 1.624131450 1.385343656
## 367 368 369 370 371 372
## 1.409390626 1.126650114 0.974262725 0.371340617 1.173783794 0.973385100
## 373 374 375 376 377 378
## 1.339886225 0.651051308 0.656613577 -0.358291420 -1.563803253 -0.593937891
## 379 380 381 382 383 384
## 0.725376915 0.908688097 1.341421727 -0.074975313 -0.721341795 0.009820264
## 385 386 387 388 389 390
## 0.970983858 0.285689868 0.895267358 0.161574217 0.666534641 -0.474948308
## 391 392 393 394 395 396
## -0.088619239 0.678475095 0.338018657 0.550802916 0.576091181 0.529517191
## 397 398 399 400 401 402
## 0.741653385 0.476480850 0.373961863 0.323679712 0.369879128 0.162712000
## 403 404 405 406 407 408
## -0.058518666 -0.104060802 -0.112017719 0.050951802 -0.131415338 0.104563859
## 409 410 411 412 413 414
## 0.053276379 -0.092777352 -0.452444396 -0.071862668 -0.144286972 -0.265169778
## 415 416 417 418 419 420
## -0.167530888 -0.119852311 -0.010592448 -0.596637775 -0.291780834 -0.572431409
## 421 422 423 424 425 426
## -0.524476802 -0.381992912 0.601516456 -0.253288587 0.828225503 0.941562372
## 427 428 429 430 431 432
## 0.332658448 0.210824121 -1.239570787 -0.167003226 -0.464695430 0.023787661
## 433 434 435 436 437 438
## -0.111491675 -0.294240202 -0.896646299 -0.745566537 -0.651616954 -0.503223045
## 439 440 441 442 443 444
## -0.347567598 0.081167828 -0.165192619 -0.553835019 -0.717276363 -0.204684507
## 445 446 447 448 449 450
## -0.802116513 -1.243301663 -1.141765058 -1.282322973 -0.579209912 -0.923876275
## 451 452 453 454 455 456
## -0.718991611 -0.369982407 -0.777400663 -0.405229759 -0.424967900 -0.763923450
## 457 458 459 460 461 462
## -0.322593050 -0.708692810 -0.594475349 -0.393429235 -0.511584162 -0.576924044
## 463 464 465 466 467 468
## -0.138878504 0.056506591 0.211944673 -0.181155200 0.361967467 0.121323581
## 469 470 471 472 473 474
## -0.021802897 0.120158880 -0.415688929 -0.265938907 -0.301744682 -0.019734757
## 475 476 477 478 479 480
## 0.262074152 -0.402834214 -0.220238248 -0.491042184 -0.527245371 -0.371250466
## 481 482 483 484 485 486
## -0.296393898 -0.496860186 -0.352586221 -0.231493563 -0.207379903 0.184858043
## 487 488
## 0.034526012 0.308302624
#mecklenburg
lowest_rmse_dl_meck <- Inf
best_mod_dl_meck <- NULL
for (q in seq(1,14)){
mod <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_meck_test[,8]),h=14,
interval = TRUE)
forecast_acc <- rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f$forecasts[,2])
if (forecast_acc<lowest_rmse_dl_meck){
lowest_rmse_dl_meck<- forecast_acc
best_mod_dl_meck <-mod
}
}
lowest_rmse_dl_meck #0.212, 0.149
## [1] 0.2122282
summary(best_mod_dl_meck) #DL(2)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9644 -0.3551 0.0139 0.3342 2.4752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.18759 0.36463 -30.682 < 2e-16 ***
## log_viral_gene.t 0.28237 0.06590 4.285 2.20e-05 ***
## log_viral_gene.1 0.11153 0.08830 1.263 0.207
## log_viral_gene.2 0.35381 0.06552 5.400 1.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6201 on 484 degrees of freedom
## Multiple R-squared: 0.6879, Adjusted R-squared: 0.686
## F-statistic: 355.7 on 3 and 484 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 924.456 945.4076
checkresiduals(best_mod_dl_meck)
## 1 2 3 4 5
## 0.0878210139 0.3800073610 0.3744189744 0.2224762173 0.1289952774
## 6 7 8 9 10
## 0.3618215647 0.4311459317 0.5173828389 0.2498647545 0.2459964098
## 11 12 13 14 15
## 0.3671665497 0.3266017253 0.3230277124 0.2624211421 0.2614478592
## 16 17 18 19 20
## 0.1417386391 0.3738787833 0.6582855570 0.5884310684 0.3534665893
## 21 22 23 24 25
## 0.1703357025 0.4721527786 0.4170098038 0.2797150439 0.3413641694
## 26 27 28 29 30
## 0.6073583852 0.8027948260 0.7231762347 0.6441895867 0.3269096718
## 31 32 33 34 35
## 0.0206588211 -0.1856444081 0.2832685352 0.0914426569 -0.1949623021
## 36 37 38 39 40
## -0.2878551098 -0.4609823114 -0.1439375704 0.0299054615 -0.1398242289
## 41 42 43 44 45
## -0.2390741351 0.0815095854 -0.0614045209 -0.1451269686 0.0422653507
## 46 47 48 49 50
## -0.1948615136 0.2187748466 -0.3628210458 -0.8106227426 -0.3819471623
## 51 52 53 54 55
## -0.3600536513 -0.0717598059 -0.1082864631 -0.2197058396 0.4153064938
## 56 57 58 59 60
## -0.0754918747 0.2162053565 -0.8626604131 -0.8104160698 -0.2226433699
## 61 62 63 64 65
## -0.8937618943 0.7697239950 1.1378736596 1.8131536285 1.8099988631
## 66 67 68 69 70
## 2.1154907044 2.2811008252 2.4752055463 1.1691885586 0.9079300138
## 71 72 73 74 75
## -0.3459719917 0.1508996029 -0.1559081837 0.3243754992 0.4766392039
## 76 77 78 79 80
## 0.5125433514 0.2646871902 0.1023414631 -0.0045949843 -0.2685873156
## 81 82 83 84 85
## -0.0848307333 -0.0385798826 0.1713571528 -0.2861106668 0.1031875596
## 86 87 88 89 90
## 0.0005460578 0.2571983271 0.0022882660 0.0337302033 0.4748384700
## 91 92 93 94 95
## 0.0980440317 0.2486419174 0.0314852899 -0.0838581626 -0.0083080292
## 96 97 98 99 100
## -0.1064370833 0.0751896500 -0.0045140084 0.3669699467 0.1785183070
## 101 102 103 104 105
## -0.2392410495 0.3561993871 -0.2358444839 0.6051792825 0.3242977958
## 106 107 108 109 110
## 0.2066500784 0.4170491229 0.1480623223 0.3974642028 0.7600343121
## 111 112 113 114 115
## 0.5112332846 0.4762998428 0.1014601380 -0.3412409831 -0.0754742015
## 116 117 118 119 120
## -0.4360419950 -0.4342811288 -0.2410305631 -0.3245172836 -0.3545028704
## 121 122 123 124 125
## -0.4460961412 -0.8274934435 -0.5853430418 -0.2160234932 0.0042513993
## 126 127 128 129 130
## -0.5306383062 0.4990229976 -0.2123754706 0.5598229002 0.5147167433
## 131 132 133 134 135
## 1.2401141341 0.5114043986 0.2890544648 -0.4902832576 -0.6081426472
## 136 137 138 139 140
## -0.2788478780 -0.7055956017 -0.6896501004 0.4039368977 -0.0619616724
## 141 142 143 144 145
## -0.4967710096 0.1963164685 0.4889487757 0.3820255160 0.7651740161
## 146 147 148 149 150
## 0.4743381872 0.2302727008 1.3486237340 0.1114170252 -0.3847607964
## 151 152 153 154 155
## -1.0716595037 0.2806894893 -0.6050143017 -0.7885182086 -1.0754080648
## 156 157 158 159 160
## -0.5830989873 -0.4349648860 -0.9086270042 -0.3056534439 0.1298147136
## 161 162 163 164 165
## 0.1624682117 0.3245212557 -0.1536432871 -0.5535588781 -0.6189787223
## 166 167 168 169 170
## -0.4108601145 -0.5681596992 -1.4326406932 -0.8976950851 -0.8651557972
## 171 172 173 174 175
## -0.8362828045 -1.3785007585 -0.6222170298 -0.2004651997 -1.0149715355
## 176 177 178 179 180
## -0.8708239731 -1.5060745936 -0.3779234002 -0.2299975404 -0.3552922621
## 181 182 183 184 185
## -0.6076610236 -0.3802574530 -0.5520942136 -0.2714904264 0.2083385043
## 186 187 188 189 190
## 0.2179882865 0.4190906633 0.0971735397 -0.3055417006 0.0115603021
## 191 192 193 194 195
## -0.1790631591 -0.0785164719 -0.1424524813 -0.2519345208 0.1824475177
## 196 197 198 199 200
## -0.0954619473 -0.0275230892 0.2401983648 0.2950517375 0.2542087654
## 201 202 203 204 205
## 0.2906126846 0.0216548838 0.1572355912 -0.0032882137 0.4562520516
## 206 207 208 209 210
## 0.4997724798 0.1509238282 0.3064077888 0.0954090561 -0.1257807871
## 211 212 213 214 215
## -0.3790084180 -0.4873693084 -0.2132264846 -0.1684593812 -0.3042875778
## 216 217 218 219 220
## 0.0440491844 0.1687394112 0.1832216449 0.5964707056 0.5211846336
## 221 222 223 224 225
## 0.3715915728 0.0069657893 -0.1513280427 0.0195084419 0.1272107407
## 226 227 228 229 230
## 0.2952290498 0.3600791085 0.5297388492 0.4871792087 0.6639204248
## 231 232 233 234 235
## 0.5330634345 0.2279048217 -0.0368473728 0.0740038324 0.3061452091
## 236 237 238 239 240
## 0.1833652147 0.1207739869 0.2244091347 0.0254349373 -0.2508751356
## 241 242 243 244 245
## 0.0136821816 -0.1360793038 -0.2601655023 -0.3476054021 -1.2323267744
## 246 247 248 249 250
## -0.3398661453 -0.2451239748 -0.2517688738 -0.1206268626 -0.0958757677
## 251 252 253 254 255
## -0.1541163964 0.0316403291 -0.0752231665 -0.3848131114 -0.1969297984
## 256 257 258 259 260
## -0.1349276013 -0.3193680544 -0.5517259829 -0.2429448878 -0.3643660672
## 261 262 263 264 265
## -0.3677536969 -0.1497141476 -0.1501457512 -0.1263816550 -0.2766910847
## 266 267 268 269 270
## -0.0176196611 -0.2765009728 0.2425566290 0.0573853432 0.0141216007
## 271 272 273 274 275
## -0.1920277090 -0.6006628496 -0.2905867876 -0.3377693707 -0.6555412071
## 276 277 278 279 280
## -0.5262880744 -0.0433097513 -0.3281500723 0.0802360317 0.1366874503
## 281 282 283 284 285
## -0.0289287982 0.2007907266 0.0484089886 0.1708490841 0.1663320321
## 286 287 288 289 290
## -0.1860313771 -0.2109119629 -0.4932488442 -0.3531522267 -1.4064850922
## 291 292 293 294 295
## -1.1532720126 -0.1330494429 -0.0033190306 -0.3634634168 -0.3550048457
## 296 297 298 299 300
## -0.0590388066 -0.5021739726 0.0842670234 0.3518348266 0.1736946037
## 301 302 303 304 305
## -0.1638730742 -0.2010613353 -1.1360668040 -0.5676220975 -0.3985995027
## 306 307 308 309 310
## -0.1872866473 0.0270202768 0.0691583115 -0.2129174022 -0.0062470079
## 311 312 313 314 315
## 0.0228906731 0.0234590896 0.0584204958 0.1027359395 -0.0140892831
## 316 317 318 319 320
## 0.2097155041 0.3508939425 0.3665036540 0.2863343792 0.4489783540
## 321 322 323 324 325
## 0.3085233704 0.2358179270 0.5033533275 0.4879103557 -0.0438926432
## 326 327 328 329 330
## 0.5388422080 1.2792482022 0.8340736175 0.6710077933 0.3941027350
## 331 332 333 334 335
## 0.3010289929 0.3252155671 0.5232905003 0.1661305372 -0.2726705901
## 336 337 338 339 340
## -0.2012880855 -0.3898541799 -0.5022516428 -0.4913300972 -0.1074613641
## 341 342 343 344 345
## -0.0348003293 0.1048526419 0.4156613099 0.2720342299 0.4898100485
## 346 347 348 349 350
## 0.6294764796 0.5540817584 0.5137900114 0.3317648112 0.5339611122
## 351 352 353 354 355
## 0.7459580002 1.0497901207 1.1976668526 0.9924092017 0.2652819621
## 356 357 358 359 360
## 1.3961882323 1.7268734658 1.8154003469 1.8537873092 1.9696396100
## 361 362 363 364 365
## 1.6321456305 1.3734573904 1.8372771601 1.3748796356 1.2851071147
## 366 367 368 369 370
## 0.6766798514 0.2939523010 0.3821186827 -0.2109714895 0.0716801269
## 371 372 373 374 375
## 0.6389329311 0.5144747557 0.7280385878 0.7234862218 0.7490553586
## 376 377 378 379 380
## 0.4305749749 -1.2557039193 -0.1819290503 0.5152550651 0.5164116182
## 381 382 383 384 385
## 0.5267622758 0.2408123778 -0.1993893489 0.2066629680 0.3977152039
## 386 387 388 389 390
## 0.2047798242 0.1569723710 0.0813437916 0.0459501676 -0.1416181932
## 391 392 393 394 395
## 0.0191113542 0.5500275194 0.1987352021 0.7297226462 0.4890137605
## 396 397 398 399 400
## 0.6558494116 0.3726109228 0.3207934548 1.0012190410 0.8052336735
## 401 402 403 404 405
## 1.2363070464 1.1523518150 0.8791922614 0.6545646600 -0.1976625334
## 406 407 408 409 410
## 0.4774693193 0.1086378007 0.2138499238 0.2113394376 0.2320715188
## 411 412 413 414 415
## 0.2024586817 0.2476425476 0.5958574009 0.6097536271 0.8810846180
## 416 417 418 419 420
## 0.7249281713 0.8731739179 -0.0377808311 -1.3841622185 -0.3319225939
## 421 422 423 424 425
## -0.7941100884 -0.7520911894 -0.4967659227 -0.7468647428 -1.1265872635
## 426 427 428 429 430
## 0.1382658891 -0.8296419141 -1.0117849156 -1.2488893370 -1.8075341017
## 431 432 433 434 435
## -1.0969729383 -0.8732810942 -1.1328422403 -1.0851673760 -0.8410658029
## 436 437 438 439 440
## 0.5757437670 -0.1673485431 -0.5650527492 -0.8413939749 -1.0939810172
## 441 442 443 444 445
## -0.7240712727 -1.1301022485 -0.8080670738 -0.6315737562 -0.8368956126
## 446 447 448 449 450
## -1.0987831437 -0.2008766537 -1.2226962410 0.1027709802 -0.2926703197
## 451 452 453 454 455
## -0.5646493951 -0.8817429341 -0.6307754280 -0.8522008641 -0.4673554302
## 456 457 458 459 460
## -0.8584311360 -0.3759321478 -0.2457658142 -0.5640702694 -1.0387994037
## 461 462 463 464 465
## -0.3312933428 0.0818168001 -0.0499004269 0.1569463603 -0.1985874568
## 466 467 468 469 470
## -0.9463877453 -1.3420041139 -1.9643629170 -1.0568113313 -0.9979023375
## 471 472 473 474 475
## -0.9311086544 -0.7326924603 -0.8322180793 -1.0314967906 -0.5993223386
## 476 477 478 479 480
## -0.1502704111 -0.4834551844 -0.3747059760 -0.4652754436 -0.6305169163
## 481 482 483 484 485
## -0.4924727479 -0.6181290957 -0.5199200960 -0.6593226135 -0.5830868700
## 486 487 488
## -0.5728043461 -0.4415182273 -0.2856220900
mod_dl13_meck <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,q=13)
summary(mod_dl13_meck)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73309 -0.33153 -0.01849 0.29939 1.86748
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12.69622 0.36233 -35.041 < 2e-16 ***
## log_viral_gene.t 0.20943 0.06059 3.456 0.000598 ***
## log_viral_gene.1 0.10162 0.08119 1.252 0.211377
## log_viral_gene.2 0.01814 0.08120 0.223 0.823341
## log_viral_gene.3 0.13229 0.08118 1.630 0.103882
## log_viral_gene.4 -0.01279 0.08116 -0.158 0.874832
## log_viral_gene.5 0.06239 0.08117 0.769 0.442470
## log_viral_gene.6 0.02190 0.08071 0.271 0.786203
## log_viral_gene.7 0.07913 0.08052 0.983 0.326239
## log_viral_gene.8 0.04023 0.08058 0.499 0.617882
## log_viral_gene.9 0.02790 0.08057 0.346 0.729321
## log_viral_gene.10 0.04824 0.08062 0.598 0.549946
## log_viral_gene.11 0.06230 0.08064 0.772 0.440224
## log_viral_gene.12 -0.02368 0.08020 -0.295 0.767941
## log_viral_gene.13 0.07544 0.05998 1.258 0.209093
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5586 on 462 degrees of freedom
## Multiple R-squared: 0.7522, Adjusted R-squared: 0.7447
## F-statistic: 100.2 on 14 and 462 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 814.8224 881.5027
f_dl13_meck <- forecast(mod_dl13_meck,
x= t(full_cases_wastewater_weather_data_meck_test[,8]),
h=14)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_dl13_meck$forecasts)
## [1] 0.3192566
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_dl13_meck$forecasts)
## [1] 0.2851718
checkresiduals(mod_dl13_meck)
## 1 2 3 4 5
## 0.1154434640 0.2270340292 0.1352352965 0.1303615803 0.0510685951
## 6 7 8 9 10
## 0.1315203487 0.4052983027 0.3961927409 0.1406918438 -0.0184856821
## 11 12 13 14 15
## 0.4249214051 0.3649271924 0.0748429973 0.1864538032 0.4611759268
## 16 17 18 19 20
## 0.5471971296 0.5095830728 0.2561405400 0.0984354697 0.1226892835
## 21 22 23 24 25
## -0.1545718404 0.3455899352 0.1406183373 -0.0769016649 -0.1017796615
## 26 27 28 29 30
## -0.3005851425 -0.0631893579 0.0373683413 -0.1490635157 -0.2746711349
## 31 32 33 34 35
## -0.0641437710 -0.1942494164 -0.4105111857 -0.1294883922 -0.3816067611
## 36 37 38 39 40
## 0.0513366351 -0.5058665684 -0.8671666250 -0.2086301484 -0.2621130355
## 41 42 43 44 45
## -0.2622951365 -0.2198464113 -0.3815319399 0.2145794599 -0.2888187268
## 46 47 48 49 50
## -0.0886916200 -1.0618606282 -0.9294641841 -0.3059824930 -0.9673356253
## 51 52 53 54 55
## 0.4786226459 0.8888609172 0.7051449141 0.9121232008 1.1884105847
## 56 57 58 59 60
## 1.4883461331 1.7798923890 0.8876330788 0.7898089310 0.6592105489
## 61 62 63 64 65
## 0.9386759679 0.8681499302 1.1211544072 1.3971857848 1.1992074642
## 66 67 68 69 70
## 0.8661658767 0.6851140186 0.4517411439 0.0743119166 0.2713356005
## 71 72 73 74 75
## 0.0868381477 0.2690146590 -0.1817420173 0.3041275630 0.1631036238
## 76 77 78 79 80
## 0.2806294629 0.0252346283 0.0168765856 0.3523197629 -0.0422787474
## 81 82 83 84 85
## -0.1059178104 -0.1600370295 0.0222768006 0.0374899407 -0.0372072494
## 86 87 88 89 90
## 0.0734926953 0.0494457678 0.2035631336 0.1302101722 -0.2156379315
## 91 92 93 94 95
## 0.3077742906 -0.2629356738 0.5856755520 0.2645592814 0.0681282556
## 96 97 98 99 100
## 0.3590388903 0.0235103853 0.2842293473 0.6780099823 0.4135143607
## 101 102 103 104 105
## 0.3955151594 0.0418059724 -0.3018305016 0.3035450425 -0.1784841753
## 106 107 108 109 110
## -0.1281243703 -0.0584270735 -0.0959087697 -0.3638632057 -0.2499124165
## 111 112 113 114 115
## -0.6312873074 -0.4452861115 -0.1259963552 -0.0294754723 -0.6486568944
## 116 117 118 119 120
## -0.3122164823 -0.7359902264 -0.2215079793 -0.1153478731 0.6795349476
## 121 122 123 124 125
## 0.1773442653 0.0600701709 -0.1889507606 -0.3097936116 0.2051331663
## 126 127 128 129 130
## -0.3375305716 -0.1608711229 0.6703004590 0.2102639144 -0.6676801351
## 131 132 133 134 135
## 0.2081887957 0.7348189866 0.5480498377 0.4667766296 0.3528875268
## 136 137 138 139 140
## 0.1350074863 1.3052752368 0.3190712057 -0.1178076547 -0.0528254602
## 141 142 143 144 145
## 0.5757944381 0.0161492465 -0.3346466580 -0.3315275269 0.0103178648
## 146 147 148 149 150
## 0.1385654475 -0.4081662802 0.0213600537 0.2785856680 0.4381865192
## 151 152 153 154 155
## 0.2902639854 -0.0483963354 -0.4370624796 -0.4269600594 0.0587650638
## 156 157 158 159 160
## -0.2269002839 -1.0032598113 -1.0994138191 -0.3511850892 -0.6148724060
## 161 162 163 164 165
## -1.1621377955 -0.4810709251 -0.2644705917 -1.0132644077 -0.8380323525
## 166 167 168 169 170
## -1.1137161570 -0.0942174231 -0.0597049633 -0.0533479763 -0.6249979097
## 171 172 173 174 175
## -0.3451893475 -0.4822907257 -0.1887738421 0.2871146244 0.3261707724
## 176 177 178 179 180
## 0.5703240099 0.4102482499 -0.0426223866 0.3533020389 0.1348035726
## 181 182 183 184 185
## 0.2319533437 0.1583455810 0.0174336244 0.6699546788 0.2408587594
## 186 187 188 189 190
## 0.3036190525 0.4429280681 0.4440327257 0.3936354323 0.4215217713
## 191 192 193 194 195
## 0.4317954116 0.4012271112 0.2458079710 0.4927100052 0.5252357846
## 196 197 198 199 200
## 0.1693024748 0.3159285588 0.3943514267 0.0976188288 -0.1418879854
## 201 202 203 204 205
## -0.1206977194 0.0140737600 -0.0033403409 -0.2246424804 0.0078717060
## 206 207 208 209 210
## 0.0574706898 0.0284970374 0.2295973935 0.1771223515 0.0475649165
## 211 212 213 214 215
## -0.2409293082 -0.2003294810 -0.0364154866 0.1410262664 0.1262449786
## 216 217 218 219 220
## 0.2703524923 0.4000392222 0.3211932411 0.4699224823 0.4082027723
## 221 222 223 224 225
## 0.1130797367 0.0616690343 0.0619215483 0.3199954451 0.1522828022
## 226 227 228 229 230
## 0.0673150840 0.1732020126 -0.0015922747 -0.2434029080 -0.0248030554
## 231 232 233 234 235
## -0.1748995223 -0.2931907728 -0.2937878893 -1.2233721708 -0.2888865323
## 236 237 238 239 240
## -0.2057416870 -0.2455276237 -0.1868723618 -0.1894794816 -0.4054396305
## 241 242 243 244 245
## -0.1864621667 -0.3464268712 -0.5808044949 -0.4494625225 -0.3465372735
## 246 247 248 249 250
## -0.5219881631 -0.6795818991 -0.4072144894 -0.4740392080 -0.6594986917
## 251 252 253 254 255
## -0.3662173995 -0.4302400871 -0.3796893668 -0.6536580513 -0.3203183959
## 256 257 258 259 260
## -0.5431666474 -0.0297483332 -0.1993672491 -0.1643963831 -0.3633078744
## 261 262 263 264 265
## -0.5932981077 -0.3165781789 -0.2997600422 -0.7190597063 -0.5570845699
## 266 267 268 269 270
## -0.1699240588 -0.4766515524 -0.3550780963 -0.1978323973 -0.3591741417
## 271 272 273 274 275
## -0.1369848419 -0.2807230695 -0.0647239886 -0.0303891845 -0.2330683495
## 276 277 278 279 280
## -0.2497993460 -0.4343118668 -0.3944618074 -1.3742536351 -1.1321409061
## 281 282 283 284 285
## -0.1243059746 0.0649356156 -0.3209308316 -0.2910931237 -0.0452687746
## 286 287 288 289 290
## -0.5063281870 0.0258508009 0.2788148558 -0.0926920569 -0.2558142424
## 291 292 293 294 295
## -0.2592924281 -0.7674038540 -0.3604768079 -0.1815794261 -0.0356889821
## 296 297 298 299 300
## -0.0714876491 0.0005602339 -0.2676355729 -0.1260995957 -0.0846714591
## 301 302 303 304 305
## -0.0767350582 0.0235402762 0.1404842677 -0.0114305765 0.2999126993
## 306 307 308 309 310
## 0.2258628904 0.3472683135 0.2338500739 0.4008778843 0.2800907637
## 311 312 313 314 315
## 0.2093030035 0.5031227312 0.4051220630 -0.1119382661 0.4839754811
## 316 317 318 319 320
## 1.2218486676 0.7935483343 0.7361709530 0.5115400839 0.7365557525
## 321 322 323 324 325
## 0.6348473258 0.9072978629 0.4875919613 0.2602226728 0.2201507143
## 326 327 328 329 330
## 0.0455444754 0.0192482907 -0.1023649558 0.1234451759 0.1496027279
## 331 332 333 334 335
## -0.0396850055 0.2993906555 0.1228609058 0.3750343526 0.4439116287
## 336 337 338 339 340
## 0.4474401233 0.4478643209 0.5314217771 0.6426221564 0.9396866941
## 341 342 343 344 345
## 1.0807834314 1.2795425619 0.9919503664 0.2390952487 1.3257238647
## 346 347 348 349 350
## 1.6582117010 1.7382339251 1.8288656699 1.8674786547 1.5405359199
## 351 352 353 354 355
## 1.2659866030 1.7227066897 1.4210764575 1.3857186361 1.4492874470
## 356 357 358 359 360
## 0.8665485288 0.9204658828 0.5620756731 0.3497518935 0.8571256600
## 361 362 363 364 365
## 0.6038809885 0.5919902011 0.4861884069 0.3972610781 0.1601925395
## 366 367 368 369 370
## -1.6965490615 -0.5914658017 0.2450075816 0.1778329267 0.2552411733
## 371 372 373 374 375
## -0.0273428988 -0.4965941114 -0.1713912626 0.0617665349 -0.1057698974
## 376 377 378 379 380
## -0.1642314360 -0.2433329984 -0.2806006880 -0.4566661748 -0.3713376271
## 381 382 383 384 385
## 0.1451190608 -0.1602316576 0.0279101382 -0.0583899848 0.1007041774
## 386 387 388 389 390
## -0.1191529073 -0.1870452845 0.5200688855 0.3996637267 0.4361169431
## 391 392 393 394 395
## 0.5711442316 0.4109962261 0.2472779619 -0.2182240622 0.4120938091
## 396 397 398 399 400
## 0.1408284270 0.0033971556 0.1218508480 0.1446594079 0.0857092846
## 401 402 403 404 405
## 0.2392272010 0.4805895070 0.4877681182 0.2615586832 0.2613297400
## 406 407 408 409 410
## 0.5213670447 -0.3031257319 -1.0884887150 -0.1297666285 -0.4855471198
## 411 412 413 414 415
## -0.6305870869 -0.3004546768 -0.6195914988 -1.0812247936 0.0832105854
## 416 417 418 419 420
## -0.8033589899 -1.0265155575 -1.0091989937 -1.7330922522 -0.9714270095
## 421 422 423 424 425
## -0.7782122871 -1.0861968333 -1.1029338163 -0.8271216764 0.1727848249
## 426 427 428 429 430
## -0.4099969807 -0.7376174045 -0.9101061610 -0.6802461435 -0.4035309941
## 431 432 433 434 435
## -0.6957691148 -0.4932027928 -0.2714978903 -0.5559209501 -0.9065429830
## 436 437 438 439 440
## -0.0865147144 -1.0772312836 0.1963166592 0.0128402944 -0.4330519803
## 441 442 443 444 445
## -0.7126733203 -0.4859006563 -0.6370821092 -0.3007303924 -0.3710199612
## 446 447 448 449 450
## -0.2396837812 -0.0267083452 -0.4286597886 -0.8771774033 -0.1981861173
## 451 452 453 454 455
## 0.2051874546 0.1103586582 0.2454179238 -0.0198330161 -0.6883519250
## 456 457 458 459 460
## -0.6038275469 -1.2853307839 -0.4356281543 -0.4561568625 -0.6124627996
## 461 462 463 464 465
## -0.5174878498 -0.7535609522 -0.9973528513 -0.7892364594 -0.3424722037
## 466 467 468 469 470
## -0.6082043324 -0.5059209299 -0.6381575460 -0.7128357867 -0.5859581855
## 471 472 473 474 475
## -0.5339275520 -0.4603546985 -0.5398331452 -0.4226189531 -0.4406174862
## 476 477
## -0.3922388130 -0.2259694150
mod_dl14_meck <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_meck_train,q=14)
summary(mod_dl14_meck)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52782 -0.33597 -0.01237 0.30179 1.98147
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12.790812 0.363314 -35.206 < 2e-16 ***
## log_viral_gene.t 0.210989 0.060327 3.497 0.000515 ***
## log_viral_gene.1 0.110288 0.080908 1.363 0.173509
## log_viral_gene.2 0.012731 0.080872 0.157 0.874982
## log_viral_gene.3 0.121994 0.080927 1.507 0.132380
## log_viral_gene.4 -0.006169 0.080849 -0.076 0.939209
## log_viral_gene.5 0.055441 0.080898 0.685 0.493492
## log_viral_gene.6 0.013397 0.080883 0.166 0.868518
## log_viral_gene.7 0.085842 0.080384 1.068 0.286125
## log_viral_gene.8 0.045452 0.080255 0.566 0.571438
## log_viral_gene.9 0.018783 0.080295 0.234 0.815143
## log_viral_gene.10 0.052275 0.080281 0.651 0.515278
## log_viral_gene.11 0.060375 0.080365 0.751 0.452877
## log_viral_gene.12 -0.024241 0.080316 -0.302 0.762928
## log_viral_gene.13 -0.056401 0.079950 -0.705 0.480886
## log_viral_gene.14 0.147705 0.059744 2.472 0.013786 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5561 on 460 degrees of freedom
## Multiple R-squared: 0.755, Adjusted R-squared: 0.747
## F-statistic: 94.51 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 809.8517 880.6638
f_dl14_meck <- forecast(mod_dl14_meck,
x= t(full_cases_wastewater_weather_data_meck_test[,8]),
h=14,interval = TRUE)
rmse(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_dl14_meck$forecasts[,2])
## [1] 0.3135576
mae(full_cases_wastewater_weather_data_meck_test$log_mean_new_cases,
f_dl14_meck$forecasts[,2])
## [1] 0.2853209
checkresiduals(mod_dl14_meck)
## 1 2 3 4 5 6
## 0.083673414 0.203715871 0.108310564 0.045605367 0.110362522 0.393824828
## 7 8 9 10 11 12
## 0.283817235 0.228569589 -0.026232304 0.407629201 0.361447059 0.052547076
## 13 14 15 16 17 18
## 0.178001206 0.472462403 0.552468387 0.433889572 0.248862452 0.077375063
## 19 20 21 22 23 24
## 0.100255268 -0.155851852 0.383149327 0.144611745 -0.141688388 -0.114885685
## 25 26 27 28 29 30
## -0.305414029 -0.073615076 0.035925731 -0.252943021 -0.244670279 0.087310528
## 31 32 33 34 35 36
## -0.197463150 -0.414951938 -0.149099555 -0.381173178 0.105180877 -0.507462204
## 37 38 39 40 41 42
## -0.927093891 -0.222960778 -0.261467804 -0.278147642 -0.227185504 -0.378278193
## 43 44 45 46 47 48
## 0.159035080 -0.273853376 -0.092976634 -1.069741022 -0.948109530 -0.306405589
## 49 50 51 52 53 54
## -0.863064403 0.480081475 0.778805931 0.711123070 0.895631949 1.175119854
## 55 56 57 58 59 60
## 1.470857538 1.673620842 0.877213084 0.798740972 0.606666470 0.926610972
## 61 62 63 64 65 66
## 0.822451538 1.109450802 1.085787869 1.182070764 0.857658253 0.731467011
## 67 68 69 70 71 72
## 0.488390679 0.108432878 0.324193401 0.536438611 0.288742072 -0.172080777
## 73 74 75 76 77 78
## 0.300727820 0.168724681 0.274726918 0.031480759 0.049598504 0.373607464
## 79 80 81 82 83 84
## -0.002866966 -0.108282393 -0.176879302 0.005139536 0.039720451 0.006671769
## 85 86 87 88 89 90
## 0.082309573 0.012106944 0.195568556 0.117092948 -0.226234898 0.304477535
## 91 92 93 94 95 96
## -0.389882718 0.613438625 0.412712740 0.057138967 0.352902740 0.008560608
## 97 98 99 100 101 102
## 0.278130924 0.602149876 0.430990641 0.419864616 0.032364319 -0.316782862
## 103 104 105 106 107 108
## 0.283565605 -0.175242847 -0.158905309 -0.037251591 -0.110680855 -0.362177583
## 109 110 111 112 113 114
## -0.254869641 -0.628388144 -0.436689816 -0.150006003 0.007474222 -0.479450536
## 115 116 117 118 119 120
## -0.311955557 -0.741149972 -0.227838354 -0.128741053 0.581673961 0.229427592
## 121 122 123 124 125 126
## 0.065854073 -0.227517218 -0.322209225 0.165986256 -0.351316573 -0.412853967
## 127 128 129 130 131 132
## 0.703709198 0.141136814 -0.637472279 0.209881186 0.749356210 0.590173817
## 133 134 135 136 137 138
## 0.642901903 0.368915261 0.176590063 1.292981938 0.296486825 -0.152654063
## 139 140 141 142 143 144
## -0.047852413 0.396782323 0.042512824 -0.140314907 -0.315514338 -0.152180505
## 145 146 147 148 149 150
## 0.139575873 -0.356172563 0.071344091 0.330071292 0.465744800 0.647180537
## 151 152 153 154 155 156
## -0.240704446 -0.433002635 -0.418524658 0.178443669 -0.202221510 -0.988534265
## 157 158 159 160 161 162
## -1.104346842 -0.378046737 -0.599136381 -1.160978629 -0.504870864 -0.218204950
## 163 164 165 166 167 168
## -0.997848618 -0.847337339 -0.970523182 -0.058223360 -0.066176988 -0.276425474
## 169 170 171 172 173 174
## -0.394131347 -0.348757251 -0.486810964 -0.184599029 0.181121759 0.341363720
## 175 176 177 178 179 180
## 0.597635822 0.554918616 -0.046330493 0.344939888 0.135983889 0.157789623
## 181 182 183 184 185 186
## 0.172392220 0.035975707 0.697702454 0.251142866 0.314330712 0.462649289
## 187 188 189 190 191 192
## 0.554286428 0.404283953 0.432232194 0.454116679 0.405956061 0.254142897
## 193 194 195 196 197 198
## 0.506486369 0.639235343 0.173128478 0.317428907 0.357183148 0.097078915
## 199 200 201 202 203 204
## -0.145247699 -0.115962461 0.152087391 -0.005357401 -0.211596058 -0.050151630
## 205 206 207 208 209 210
## 0.056863765 0.037783605 0.240534616 0.288189768 0.043790436 -0.240101494
## 211 212 213 214 215 216
## -0.157707365 -0.056896908 0.125865046 0.109479264 0.211576331 0.394874826
## 217 218 219 220 221 222
## 0.324116687 0.368418890 0.408429453 0.104188411 0.054861850 0.144561498
## 223 224 225 226 227 228
## 0.321135690 0.158932473 0.006441350 0.161730015 -0.014472257 -0.247536562
## 229 230 231 232 233 234
## -0.058038082 -0.174460627 -0.280441817 -0.218221623 -1.236400020 -0.303947449
## 235 236 237 238 239 240
## -0.212385134 -0.267329530 -0.187324705 -0.174693433 -0.379732549 -0.198600813
## 241 242 243 244 245 246
## -0.355265131 -0.588452008 -0.407572550 -0.358375338 -0.520762780 -0.680479784
## 247 248 249 250 251 252
## -0.425806851 -0.490049514 -0.671583984 -0.429451793 -0.435406359 -0.394451973
## 253 254 255 256 257 258
## -0.648419830 -0.339791705 -0.554080852 -0.044116526 -0.192096899 -0.179573145
## 259 260 261 262 263 264
## -0.367558237 -0.675288139 -0.331304639 -0.313166651 -0.728111349 -0.611805831
## 265 266 267 268 269 270
## -0.168956313 -0.458199417 -0.367018295 -0.211525045 -0.361337641 -0.143816302
## 271 272 273 274 275 276
## -0.244640382 -0.077397245 -0.029399448 -0.277802980 -0.267612959 -0.450998155
## 277 278 279 280 281 282
## -0.408262589 -1.499252712 -1.129477922 -0.112450865 0.039643067 -0.324413390
## 283 284 285 286 287 288
## -0.290525830 -0.041874533 -0.459955189 0.027960488 0.297860449 -0.112198979
## 289 290 291 292 293 294
## -0.267310416 -0.273467438 -0.776781816 -0.342723799 -0.185990398 -0.008966314
## 295 296 297 298 299 300
## -0.075112821 -0.005481946 -0.272122270 -0.122574727 -0.174129075 -0.065889338
## 301 302 303 304 305 306
## 0.047714726 0.298739868 -0.025017908 0.289811610 0.217793082 0.239615121
## 307 308 309 310 311 312
## 0.239571458 0.414151066 0.257634125 0.204833149 0.506767865 0.406909890
## 313 314 315 316 317 318
## -0.057258669 0.482213312 1.231821470 0.721636017 0.728648391 0.500368238
## 319 320 321 322 323 324
## 0.731164422 0.642727538 0.907181007 0.502277235 0.234604449 0.227290927
## 325 326 327 328 329 330
## 0.041763187 0.034718302 -0.090580190 0.144835121 0.191011942 0.117674808
## 331 332 333 334 335 336
## 0.296869566 0.125979818 0.381965504 0.525056634 0.443657128 0.454052683
## 337 338 339 340 341 342
## 0.586118672 0.628964184 0.923735461 1.072776733 1.185790856 0.998244704
## 343 344 345 346 347 348
## 0.253340933 1.331491217 1.652599841 1.737726257 1.830308586 1.981473344
## 349 350 351 352 353 354
## 1.532152911 1.272594809 1.682241025 1.404727965 1.354108842 1.432703322
## 355 356 357 358 359 360
## 0.857938160 0.905015563 0.588338824 0.397328873 0.853828081 0.610746309
## 361 362 363 364 365 366
## 0.621299482 0.476321744 0.409339184 0.197701568 -1.422533507 -0.616534030
## 367 368 369 370 371 372
## 0.223464548 0.300899504 0.100463617 -0.048853561 -0.501220205 -0.265002792
## 373 374 375 376 377 378
## 0.038305076 -0.124335803 -0.181012347 -0.264522309 -0.295319384 -0.454387699
## 379 380 381 382 383 384
## -0.375987394 0.119548942 -0.173341685 0.010694421 -0.135396856 0.088129302
## 385 386 387 388 389 390
## -0.122878115 -0.224254237 0.491590967 0.390222335 0.413354790 0.507118521
## 391 392 393 394 395 396
## 0.390756165 0.224829384 -0.395754231 0.394496872 0.131855036 -0.010801313
## 397 398 399 400 401 402
## 0.093833413 0.137200493 0.081621831 0.060338738 0.480498679 0.507988234
## 403 404 405 406 407 408
## 0.272410677 0.368974209 0.515291904 -0.319724897 -1.206895697 -0.137937622
## 409 410 411 412 413 414
## -0.489106405 -0.636590369 -0.282526529 -0.618754014 -1.073271939 -0.120288440
## 415 416 417 418 419 420
## -0.796112808 -1.013106913 -0.995653753 -1.527820192 -0.975681290 -0.760436347
## 421 422 423 424 425 426
## -1.135932461 -1.105016648 -0.818919288 0.181468417 -0.490653826 -0.725625459
## 427 428 429 430 431 432
## -0.903965703 -0.619550178 -0.408564854 -0.701227412 -0.496222007 -0.290672830
## 433 434 435 436 437 438
## -0.547162448 -0.890290220 -0.228505158 -1.064244357 0.213677325 0.033515382
## 439 440 441 442 443 444
## -0.217047684 -0.711160301 -0.465666053 -0.649149701 -0.309713911 -0.370760781
## 445 446 447 448 449 450
## -0.226032639 -0.077406740 -0.409509028 -0.842848432 -0.124986960 0.201279365
## 451 452 453 454 455 456
## 0.119362479 0.250029094 -0.013946757 -0.695203647 -0.479920168 -1.362543319
## 457 458 459 460 461 462
## -0.437744273 -0.441604822 -0.580462180 -0.474034803 -0.742117255 -0.958541231
## 463 464 465 466 467 468
## -0.784336697 -0.334692619 -0.592994945 -0.270884088 -0.603632500 -0.728979911
## 469 470 471 472 473 474
## -0.588428646 -0.612960962 -0.473513648 -0.557718658 -0.430461009 -0.501864842
## 475 476
## -0.389870632 -0.205309993
exp(f_dl14_meck$forecasts[1,2])
## [1] 4.929395
exp(f_dl14_meck$forecasts[1,1])
## [1] 1.590384
exp(f_dl14_meck$forecasts[1,3])
## [1] 14.41146
exp(f_dl14_meck$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_meck_test[1,7])
## [1] 1.903267
exp(f_dl14_meck$forecasts[7,2])
## [1] 5.127421
exp(f_dl14_meck$forecasts[7,1])
## [1] 1.602196
exp(f_dl14_meck$forecasts[7,3])
## [1] 13.41248
exp(f_dl14_meck$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_meck_test[7,7])
## [1] 1.272963
exp(f_dl14_meck$forecasts[14,2])
## [1] 4.977879
exp(f_dl14_meck$forecasts[14,1])
## [1] 1.613458
exp(f_dl14_meck$forecasts[14,3])
## [1] 13.98632
exp(f_dl14_meck$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_meck_test[14,7])
## [1] 1.957939
#New Hanover
lowest_rmse_dl_hanover <- Inf
best_mod_dl_hanover <- NULL
for (q in seq(1,14)){
mod <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,q=q)
f <- forecast(mod, x= t(full_cases_wastewater_weather_data_hanover_test[,7]),h=14)
forecast_acc <- mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f$forecasts)
if (forecast_acc<lowest_rmse_dl_hanover){
lowest_rmse_dl_hanover<- forecast_acc
best_mod_dl_hanover <-mod
}
}
lowest_rmse_dl_hanover #0.581,0.449
## [1] 0.4490573
summary(best_mod_dl_hanover) #DL(14)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.92770 -0.54283 0.01895 0.56104 1.54669
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.275542 0.323175 -25.607 <2e-16 ***
## log_viral_gene.t 0.162004 0.059146 2.739 0.0064 **
## log_viral_gene.1 0.035519 0.080932 0.439 0.6610
## log_viral_gene.2 -0.008743 0.081057 -0.108 0.9141
## log_viral_gene.3 0.056927 0.082394 0.691 0.4900
## log_viral_gene.4 0.109439 0.082429 1.328 0.1849
## log_viral_gene.5 0.008675 0.083221 0.104 0.9170
## log_viral_gene.6 0.019041 0.083370 0.228 0.8194
## log_viral_gene.7 0.022755 0.083408 0.273 0.7851
## log_viral_gene.8 0.091259 0.083419 1.094 0.2745
## log_viral_gene.9 -0.050251 0.083424 -0.602 0.5472
## log_viral_gene.10 0.020449 0.082742 0.247 0.8049
## log_viral_gene.11 0.091420 0.082722 1.105 0.2697
## log_viral_gene.12 0.013366 0.081523 0.164 0.8698
## log_viral_gene.13 -0.012672 0.081525 -0.155 0.8765
## log_viral_gene.14 0.031479 0.059567 0.528 0.5974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7457 on 460 degrees of freedom
## Multiple R-squared: 0.6205, Adjusted R-squared: 0.6082
## F-statistic: 50.15 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1089.257 1160.069
tsdisplay(residuals(best_mod_dl_hanover))
## 1 2 3 4 5 6
## 0.747671788 0.307641508 0.378269471 0.473802219 0.619452137 0.711640715
## 7 8 9 10 11 12
## 0.784764229 0.851181386 0.587009244 0.494110837 0.452150818 0.244520123
## 13 14 15 16 17 18
## 1.122428761 0.583604437 0.912896054 0.215617235 0.691798693 0.600442412
## 19 20 21 22 23 24
## 0.524673916 0.873202989 1.163039524 1.087161000 0.647565642 0.586902041
## 25 26 27 28 29 30
## 0.787283320 0.752887310 0.961409396 0.688481219 0.380161119 0.573329284
## 31 32 33 34 35 36
## 0.443081736 0.358261805 0.027539317 0.293750417 -0.150229915 0.271321532
## 37 38 39 40 41 42
## 0.122643563 -0.191472098 0.266413213 -0.044373382 0.366898659 0.576119311
## 43 44 45 46 47 48
## 0.673770853 0.442499814 0.353702994 0.518073738 0.721501191 1.016752586
## 49 50 51 52 53 54
## 0.968241689 0.797826891 0.564507013 1.403061846 1.371784098 1.189120163
## 55 56 57 58 59 60
## 0.831064425 1.273177601 0.966582768 0.844717559 1.023075623 0.807142418
## 61 62 63 64 65 66
## 1.018402414 1.150247042 1.277706262 1.143776243 0.986930140 1.396903771
## 67 68 69 70 71 72
## 1.453890134 1.287967088 1.252050855 1.127398886 1.351576932 1.109953607
## 73 74 75 76 77 78
## 1.439402548 0.826177275 0.798481506 0.559887259 0.878814915 0.460054856
## 79 80 81 82 83 84
## 0.618189988 0.354178901 0.800934551 0.644800810 0.272745138 0.556436014
## 85 86 87 88 89 90
## 0.698699805 0.765819983 0.676171855 0.678981448 0.541217929 0.878639863
## 91 92 93 94 95 96
## 0.480107399 -0.567074083 0.835251043 0.443114773 0.798032497 0.475458293
## 97 98 99 100 101 102
## 0.929089500 1.151674303 -0.365146410 1.092744210 0.958868595 0.975938609
## 103 104 105 106 107 108
## 0.727230555 0.924896703 0.191074765 0.630066217 0.830326618 0.300237101
## 109 110 111 112 113 114
## 0.431653877 -0.470709044 0.587993289 0.713496419 0.170954979 0.864112086
## 115 116 117 118 119 120
## 0.419857150 0.941106815 0.304678257 0.619942958 0.000665306 0.049049003
## 121 122 123 124 125 126
## 0.532278958 -0.483855497 -0.438958916 0.642657182 0.719306023 0.083623883
## 127 128 129 130 131 132
## 0.142308364 -0.547859467 0.679362968 -0.466719588 0.386998573 -0.101381340
## 133 134 135 136 137 138
## 0.172972328 0.335315478 -0.049409208 -0.011413372 0.034182159 -0.186190837
## 139 140 141 142 143 144
## -0.077516488 0.206178558 0.216607175 -0.276560341 -0.139998257 -0.212428313
## 145 146 147 148 149 150
## 0.010084704 0.058939187 0.568749793 0.651043913 -0.375174713 -0.182188461
## 151 152 153 154 155 156
## -0.276029586 -0.002888015 0.087513971 0.351314577 0.403895340 -0.027424995
## 157 158 159 160 161 162
## -0.004155429 0.089282066 0.116703756 -0.267717173 0.613447150 0.103826154
## 163 164 165 166 167 168
## -0.584795668 -0.797745125 -0.923444321 -0.080705315 -0.362428882 -0.193055134
## 169 170 171 172 173 174
## -0.022549817 -0.528540196 0.017414671 -0.263990755 -0.635740946 -1.006383371
## 175 176 177 178 179 180
## -0.719630746 0.041794680 -0.919307011 -1.240639400 0.153899524 -0.275186941
## 181 182 183 184 185 186
## 0.255706766 -0.622651534 -1.010647658 -1.643449840 -0.706496720 -0.554271322
## 187 188 189 190 191 192
## 0.085125471 -0.153401590 0.196242232 0.466242979 0.101916302 0.132891233
## 193 194 195 196 197 198
## -0.058730517 0.226849953 0.092034675 0.046388800 0.320837843 0.197634154
## 199 200 201 202 203 204
## 0.041543478 -0.084591895 -0.031534623 0.376878462 0.083499436 0.131331710
## 205 206 207 208 209 210
## 0.125611940 0.160134357 -0.025976111 -0.147004743 0.102707357 -0.132043750
## 211 212 213 214 215 216
## 0.142449049 0.222082014 -0.095722886 -0.086447134 0.193431092 0.047369108
## 217 218 219 220 221 222
## -0.236510673 -0.011232245 0.630867557 0.965698775 0.842951821 0.980329919
## 223 224 225 226 227 228
## 0.405603758 -0.081259496 0.020476796 0.198995617 0.539530739 0.695241902
## 229 230 231 232 233 234
## 0.505353089 0.103543071 0.084199783 -0.060773234 -0.687262335 0.223897168
## 235 236 237 238 239 240
## 0.158265282 -0.097488959 -0.063130119 -0.320686525 -0.111602996 0.223043923
## 241 242 243 244 245 246
## 0.069286926 -0.075827417 -0.195341651 0.007382603 -0.155997697 -0.340909232
## 247 248 249 250 251 252
## -0.313957509 -0.278744127 -0.331574026 -0.279316587 -0.669261650 -0.511348060
## 253 254 255 256 257 258
## -0.543592370 -0.567951602 -0.649225670 -0.795434355 -1.068118107 -0.536898969
## 259 260 261 262 263 264
## -0.781653867 -1.378215169 -0.642796987 -0.695479334 -1.133816241 -0.705216939
## 265 266 267 268 269 270
## -0.833183745 -0.481082101 -0.949364510 -0.666934935 -0.729533596 -0.670244008
## 271 272 273 274 275 276
## -0.459775767 -0.312795933 -0.683795518 -0.958265199 -0.710554591 -0.461965690
## 277 278 279 280 281 282
## -1.927703353 -1.860354405 -1.788623255 -0.580177525 -1.364166882 -1.264233742
## 283 284 285 286 287 288
## -1.405559426 -0.994684914 -1.846049333 -1.169577240 -1.522802689 -1.370957154
## 289 290 291 292 293 294
## -1.488322029 -0.898873445 -1.182528558 -1.869183395 -1.303331789 -0.838020471
## 295 296 297 298 299 300
## -0.783640584 -0.184541374 -0.804762372 -0.845862677 -0.639393492 -0.073034083
## 301 302 303 304 305 306
## 0.505106704 -0.414760325 -0.152886163 0.011629339 0.175510337 0.008692918
## 307 308 309 310 311 312
## -0.466941362 -0.303730275 0.212979426 -0.354538102 -0.630846915 -0.610448748
## 313 314 315 316 317 318
## -1.751952004 -1.272773337 -0.374306882 0.290963727 0.046446696 -0.214981661
## 319 320 321 322 323 324
## -0.545341288 -0.332527264 -0.469964243 -0.455682589 -0.018678859 -0.219464918
## 325 326 327 328 329 330
## -0.255516321 0.299562431 0.462774125 -0.712331746 0.204310949 0.378700005
## 331 332 333 334 335 336
## 0.236595198 0.131521713 0.023084524 0.309143039 0.393019139 0.514684828
## 337 338 339 340 341 342
## 0.709765643 0.815688120 0.422194522 0.927938263 1.026089235 0.119582660
## 343 344 345 346 347 348
## -0.400948873 0.618876707 1.283429018 1.428341833 1.416771338 1.546686323
## 349 350 351 352 353 354
## 0.844014152 0.520292465 0.964667125 1.468735348 1.440001829 1.088767430
## 355 356 357 358 359 360
## 1.381710323 1.285408988 0.927875505 0.875859442 1.146208669 1.053124920
## 361 362 363 364 365 366
## 0.992434881 1.103931611 1.235399280 0.792817833 0.536064069 1.022193226
## 367 368 369 370 371 372
## 1.369988900 1.386744406 1.145528674 0.111164949 -0.122587151 0.403142012
## 373 374 375 376 377 378
## 0.917741437 0.574358546 0.414126633 0.390922055 0.409998132 -0.047921889
## 379 380 381 382 383 384
## 0.051743407 0.346350681 0.219834318 0.183649959 0.003918620 -0.087689089
## 385 386 387 388 389 390
## -0.443879508 -0.368255592 -0.233817769 -0.134835441 -0.394255333 -0.319883083
## 391 392 393 394 395 396
## -0.218698343 -0.910699733 -0.465972929 -0.585333047 -0.694596814 -0.586108231
## 397 398 399 400 401 402
## -0.738585332 -0.679538577 -1.118610524 -0.420766359 -0.638185474 -0.714555809
## 403 404 405 406 407 408
## -0.585440652 -0.563505308 -0.878102761 -1.280603695 -1.191681077 -0.934102963
## 409 410 411 412 413 414
## -1.596363594 -1.557809531 -0.722601433 -1.255975639 -0.770097847 -0.727531531
## 415 416 417 418 419 420
## -0.518165467 -1.293445438 -0.778215674 -0.565879295 -0.856861437 -0.400860881
## 421 422 423 424 425 426
## -0.440988575 -0.959018978 -0.689239873 -0.689466316 -0.532029981 -0.278728684
## 427 428 429 430 431 432
## 0.266328315 0.783612944 -0.362063857 -0.402825267 -0.403869896 -0.366283882
## 433 434 435 436 437 438
## -0.063202851 0.165020700 0.151977809 -0.472627095 -0.542580764 -0.820343633
## 439 440 441 442 443 444
## -0.583075855 -0.521115134 -0.403670372 -0.526089683 -0.566016826 -1.104702309
## 445 446 447 448 449 450
## -0.806441249 -0.082094347 -0.979519688 -0.878787309 -0.900340594 -0.696046618
## 451 452 453 454 455 456
## -0.459637216 0.026626468 -0.546385035 -0.882709570 -1.394742797 -1.432171235
## 457 458 459 460 461 462
## -0.853846173 -0.715528872 -1.211671395 -1.384127172 -1.836427085 -0.407158641
## 463 464 465 466 467 468
## -1.607260055 -0.880169779 -0.844179745 -0.666642593 -0.660131954 -0.278294858
## 469 470 471 472 473 474
## -1.266666170 -1.041434986 -0.633569678 -0.426953761 -0.315162411 -0.559516785
## 475 476
## -0.196315618 -0.496435946
mod_dl14_hanover <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,q=14)
summary(mod_dl14_hanover)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.92770 -0.54283 0.01895 0.56104 1.54669
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.275542 0.323175 -25.607 <2e-16 ***
## log_viral_gene.t 0.162004 0.059146 2.739 0.0064 **
## log_viral_gene.1 0.035519 0.080932 0.439 0.6610
## log_viral_gene.2 -0.008743 0.081057 -0.108 0.9141
## log_viral_gene.3 0.056927 0.082394 0.691 0.4900
## log_viral_gene.4 0.109439 0.082429 1.328 0.1849
## log_viral_gene.5 0.008675 0.083221 0.104 0.9170
## log_viral_gene.6 0.019041 0.083370 0.228 0.8194
## log_viral_gene.7 0.022755 0.083408 0.273 0.7851
## log_viral_gene.8 0.091259 0.083419 1.094 0.2745
## log_viral_gene.9 -0.050251 0.083424 -0.602 0.5472
## log_viral_gene.10 0.020449 0.082742 0.247 0.8049
## log_viral_gene.11 0.091420 0.082722 1.105 0.2697
## log_viral_gene.12 0.013366 0.081523 0.164 0.8698
## log_viral_gene.13 -0.012672 0.081525 -0.155 0.8765
## log_viral_gene.14 0.031479 0.059567 0.528 0.5974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7457 on 460 degrees of freedom
## Multiple R-squared: 0.6205, Adjusted R-squared: 0.6082
## F-statistic: 50.15 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1089.257 1160.069
f_dl14_hanover <- forecast(mod_dl14_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,7]),
h=14,interval = TRUE)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl14_hanover$forecasts[,2])
## [1] 0.5808326
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl14_hanover$forecasts[,2])
## [1] 0.4490573
checkresiduals(mod_dl14_hanover)
## 1 2 3 4 5 6
## 0.747671788 0.307641508 0.378269471 0.473802219 0.619452137 0.711640715
## 7 8 9 10 11 12
## 0.784764229 0.851181386 0.587009244 0.494110837 0.452150818 0.244520123
## 13 14 15 16 17 18
## 1.122428761 0.583604437 0.912896054 0.215617235 0.691798693 0.600442412
## 19 20 21 22 23 24
## 0.524673916 0.873202989 1.163039524 1.087161000 0.647565642 0.586902041
## 25 26 27 28 29 30
## 0.787283320 0.752887310 0.961409396 0.688481219 0.380161119 0.573329284
## 31 32 33 34 35 36
## 0.443081736 0.358261805 0.027539317 0.293750417 -0.150229915 0.271321532
## 37 38 39 40 41 42
## 0.122643563 -0.191472098 0.266413213 -0.044373382 0.366898659 0.576119311
## 43 44 45 46 47 48
## 0.673770853 0.442499814 0.353702994 0.518073738 0.721501191 1.016752586
## 49 50 51 52 53 54
## 0.968241689 0.797826891 0.564507013 1.403061846 1.371784098 1.189120163
## 55 56 57 58 59 60
## 0.831064425 1.273177601 0.966582768 0.844717559 1.023075623 0.807142418
## 61 62 63 64 65 66
## 1.018402414 1.150247042 1.277706262 1.143776243 0.986930140 1.396903771
## 67 68 69 70 71 72
## 1.453890134 1.287967088 1.252050855 1.127398886 1.351576932 1.109953607
## 73 74 75 76 77 78
## 1.439402548 0.826177275 0.798481506 0.559887259 0.878814915 0.460054856
## 79 80 81 82 83 84
## 0.618189988 0.354178901 0.800934551 0.644800810 0.272745138 0.556436014
## 85 86 87 88 89 90
## 0.698699805 0.765819983 0.676171855 0.678981448 0.541217929 0.878639863
## 91 92 93 94 95 96
## 0.480107399 -0.567074083 0.835251043 0.443114773 0.798032497 0.475458293
## 97 98 99 100 101 102
## 0.929089500 1.151674303 -0.365146410 1.092744210 0.958868595 0.975938609
## 103 104 105 106 107 108
## 0.727230555 0.924896703 0.191074765 0.630066217 0.830326618 0.300237101
## 109 110 111 112 113 114
## 0.431653877 -0.470709044 0.587993289 0.713496419 0.170954979 0.864112086
## 115 116 117 118 119 120
## 0.419857150 0.941106815 0.304678257 0.619942958 0.000665306 0.049049003
## 121 122 123 124 125 126
## 0.532278958 -0.483855497 -0.438958916 0.642657182 0.719306023 0.083623883
## 127 128 129 130 131 132
## 0.142308364 -0.547859467 0.679362968 -0.466719588 0.386998573 -0.101381340
## 133 134 135 136 137 138
## 0.172972328 0.335315478 -0.049409208 -0.011413372 0.034182159 -0.186190837
## 139 140 141 142 143 144
## -0.077516488 0.206178558 0.216607175 -0.276560341 -0.139998257 -0.212428313
## 145 146 147 148 149 150
## 0.010084704 0.058939187 0.568749793 0.651043913 -0.375174713 -0.182188461
## 151 152 153 154 155 156
## -0.276029586 -0.002888015 0.087513971 0.351314577 0.403895340 -0.027424995
## 157 158 159 160 161 162
## -0.004155429 0.089282066 0.116703756 -0.267717173 0.613447150 0.103826154
## 163 164 165 166 167 168
## -0.584795668 -0.797745125 -0.923444321 -0.080705315 -0.362428882 -0.193055134
## 169 170 171 172 173 174
## -0.022549817 -0.528540196 0.017414671 -0.263990755 -0.635740946 -1.006383371
## 175 176 177 178 179 180
## -0.719630746 0.041794680 -0.919307011 -1.240639400 0.153899524 -0.275186941
## 181 182 183 184 185 186
## 0.255706766 -0.622651534 -1.010647658 -1.643449840 -0.706496720 -0.554271322
## 187 188 189 190 191 192
## 0.085125471 -0.153401590 0.196242232 0.466242979 0.101916302 0.132891233
## 193 194 195 196 197 198
## -0.058730517 0.226849953 0.092034675 0.046388800 0.320837843 0.197634154
## 199 200 201 202 203 204
## 0.041543478 -0.084591895 -0.031534623 0.376878462 0.083499436 0.131331710
## 205 206 207 208 209 210
## 0.125611940 0.160134357 -0.025976111 -0.147004743 0.102707357 -0.132043750
## 211 212 213 214 215 216
## 0.142449049 0.222082014 -0.095722886 -0.086447134 0.193431092 0.047369108
## 217 218 219 220 221 222
## -0.236510673 -0.011232245 0.630867557 0.965698775 0.842951821 0.980329919
## 223 224 225 226 227 228
## 0.405603758 -0.081259496 0.020476796 0.198995617 0.539530739 0.695241902
## 229 230 231 232 233 234
## 0.505353089 0.103543071 0.084199783 -0.060773234 -0.687262335 0.223897168
## 235 236 237 238 239 240
## 0.158265282 -0.097488959 -0.063130119 -0.320686525 -0.111602996 0.223043923
## 241 242 243 244 245 246
## 0.069286926 -0.075827417 -0.195341651 0.007382603 -0.155997697 -0.340909232
## 247 248 249 250 251 252
## -0.313957509 -0.278744127 -0.331574026 -0.279316587 -0.669261650 -0.511348060
## 253 254 255 256 257 258
## -0.543592370 -0.567951602 -0.649225670 -0.795434355 -1.068118107 -0.536898969
## 259 260 261 262 263 264
## -0.781653867 -1.378215169 -0.642796987 -0.695479334 -1.133816241 -0.705216939
## 265 266 267 268 269 270
## -0.833183745 -0.481082101 -0.949364510 -0.666934935 -0.729533596 -0.670244008
## 271 272 273 274 275 276
## -0.459775767 -0.312795933 -0.683795518 -0.958265199 -0.710554591 -0.461965690
## 277 278 279 280 281 282
## -1.927703353 -1.860354405 -1.788623255 -0.580177525 -1.364166882 -1.264233742
## 283 284 285 286 287 288
## -1.405559426 -0.994684914 -1.846049333 -1.169577240 -1.522802689 -1.370957154
## 289 290 291 292 293 294
## -1.488322029 -0.898873445 -1.182528558 -1.869183395 -1.303331789 -0.838020471
## 295 296 297 298 299 300
## -0.783640584 -0.184541374 -0.804762372 -0.845862677 -0.639393492 -0.073034083
## 301 302 303 304 305 306
## 0.505106704 -0.414760325 -0.152886163 0.011629339 0.175510337 0.008692918
## 307 308 309 310 311 312
## -0.466941362 -0.303730275 0.212979426 -0.354538102 -0.630846915 -0.610448748
## 313 314 315 316 317 318
## -1.751952004 -1.272773337 -0.374306882 0.290963727 0.046446696 -0.214981661
## 319 320 321 322 323 324
## -0.545341288 -0.332527264 -0.469964243 -0.455682589 -0.018678859 -0.219464918
## 325 326 327 328 329 330
## -0.255516321 0.299562431 0.462774125 -0.712331746 0.204310949 0.378700005
## 331 332 333 334 335 336
## 0.236595198 0.131521713 0.023084524 0.309143039 0.393019139 0.514684828
## 337 338 339 340 341 342
## 0.709765643 0.815688120 0.422194522 0.927938263 1.026089235 0.119582660
## 343 344 345 346 347 348
## -0.400948873 0.618876707 1.283429018 1.428341833 1.416771338 1.546686323
## 349 350 351 352 353 354
## 0.844014152 0.520292465 0.964667125 1.468735348 1.440001829 1.088767430
## 355 356 357 358 359 360
## 1.381710323 1.285408988 0.927875505 0.875859442 1.146208669 1.053124920
## 361 362 363 364 365 366
## 0.992434881 1.103931611 1.235399280 0.792817833 0.536064069 1.022193226
## 367 368 369 370 371 372
## 1.369988900 1.386744406 1.145528674 0.111164949 -0.122587151 0.403142012
## 373 374 375 376 377 378
## 0.917741437 0.574358546 0.414126633 0.390922055 0.409998132 -0.047921889
## 379 380 381 382 383 384
## 0.051743407 0.346350681 0.219834318 0.183649959 0.003918620 -0.087689089
## 385 386 387 388 389 390
## -0.443879508 -0.368255592 -0.233817769 -0.134835441 -0.394255333 -0.319883083
## 391 392 393 394 395 396
## -0.218698343 -0.910699733 -0.465972929 -0.585333047 -0.694596814 -0.586108231
## 397 398 399 400 401 402
## -0.738585332 -0.679538577 -1.118610524 -0.420766359 -0.638185474 -0.714555809
## 403 404 405 406 407 408
## -0.585440652 -0.563505308 -0.878102761 -1.280603695 -1.191681077 -0.934102963
## 409 410 411 412 413 414
## -1.596363594 -1.557809531 -0.722601433 -1.255975639 -0.770097847 -0.727531531
## 415 416 417 418 419 420
## -0.518165467 -1.293445438 -0.778215674 -0.565879295 -0.856861437 -0.400860881
## 421 422 423 424 425 426
## -0.440988575 -0.959018978 -0.689239873 -0.689466316 -0.532029981 -0.278728684
## 427 428 429 430 431 432
## 0.266328315 0.783612944 -0.362063857 -0.402825267 -0.403869896 -0.366283882
## 433 434 435 436 437 438
## -0.063202851 0.165020700 0.151977809 -0.472627095 -0.542580764 -0.820343633
## 439 440 441 442 443 444
## -0.583075855 -0.521115134 -0.403670372 -0.526089683 -0.566016826 -1.104702309
## 445 446 447 448 449 450
## -0.806441249 -0.082094347 -0.979519688 -0.878787309 -0.900340594 -0.696046618
## 451 452 453 454 455 456
## -0.459637216 0.026626468 -0.546385035 -0.882709570 -1.394742797 -1.432171235
## 457 458 459 460 461 462
## -0.853846173 -0.715528872 -1.211671395 -1.384127172 -1.836427085 -0.407158641
## 463 464 465 466 467 468
## -1.607260055 -0.880169779 -0.844179745 -0.666642593 -0.660131954 -0.278294858
## 469 470 471 472 473 474
## -1.266666170 -1.041434986 -0.633569678 -0.426953761 -0.315162411 -0.559516785
## 475 476
## -0.196315618 -0.496435946
exp(f_dl14_hanover$forecasts[1,2])
## [1] 2.365621
exp(f_dl14_hanover$forecasts[1,1])
## [1] 0.5306325
exp(f_dl14_hanover$forecasts[1,3])
## [1] 9.101989
exp(f_dl14_hanover$forecasts[1,2]) - exp(full_cases_wastewater_weather_data_hanover_test[1,6])
## [1] 1.257414
exp(f_dl14_hanover$forecasts[7,2])
## [1] 2.88277
exp(f_dl14_hanover$forecasts[7,1])
## [1] 0.6819826
exp(f_dl14_hanover$forecasts[7,3])
## [1] 11.4008
exp(f_dl14_hanover$forecasts[7,2]) - exp(full_cases_wastewater_weather_data_hanover_test[7,6])
## [1] 0.6243629
exp(f_dl14_hanover$forecasts[14,2])
## [1] 3.742474
exp(f_dl14_hanover$forecasts[14,1])
## [1] 0.8179684
exp(f_dl14_hanover$forecasts[14,3])
## [1] 15.20064
exp(f_dl14_hanover$forecasts[14,2]) - exp(full_cases_wastewater_weather_data_hanover_test[14,6])
## [1] 2.903247
mod_dl2_hanover <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
q=2)
summary(mod_dl2_hanover)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.00543 -0.54939 0.01187 0.60816 1.80704
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.336034 0.316832 -23.154 < 2e-16 ***
## log_viral_gene.t 0.254708 0.060181 4.232 2.77e-05 ***
## log_viral_gene.1 0.006965 0.083828 0.083 0.934
## log_viral_gene.2 0.266634 0.060184 4.430 1.16e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7937 on 484 degrees of freedom
## Multiple R-squared: 0.5591, Adjusted R-squared: 0.5564
## F-statistic: 204.6 on 3 and 484 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1165.335 1186.286
f_dl2_hanover <- forecast(mod_dl2_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl2_hanover$forecasts)
## [1] 0.6313079
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl2_hanover$forecasts)
## [1] 0.5276261
checkresiduals(mod_dl2_hanover)
## 1 2 3 4 5 6
## 1.074904378 0.909580304 0.813942755 0.847367928 0.915176778 0.825297521
## 7 8 9 10 11 12
## 0.512100817 0.364578861 0.554887522 0.800847849 0.692634327 0.811843633
## 13 14 15 16 17 18
## 0.754998314 0.319176751 0.415253152 0.485187186 0.685511485 0.769046660
## 19 20 21 22 23 24
## 0.853513255 0.886242227 0.591169007 0.530373813 0.388556736 0.239233951
## 25 26 27 28 29 30
## 1.212386581 0.640055757 1.185694520 0.439720833 0.907900024 0.759105273
## 31 32 33 34 35 36
## 0.768706013 1.110752752 1.070964950 1.043351598 0.711022728 0.577947075
## 37 38 39 40 41 42
## 0.849282961 0.826891381 1.019611241 0.491621656 0.187619626 0.513869464
## 43 44 45 46 47 48
## 0.363113094 0.301199723 0.036692991 0.303271139 -0.194842763 0.233089707
## 49 50 51 52 53 54
## 0.224898882 -0.102113259 0.633930112 0.309632108 0.587484382 0.731570072
## 55 56 57 58 59 60
## 0.790867520 0.533382024 0.367530334 0.521603643 0.977218594 1.123166756
## 61 62 63 64 65 66
## 1.684570018 1.372199738 0.837337619 1.705404861 1.509916382 1.168745119
## 67 68 69 70 71 72
## 0.692708975 0.721212296 0.450098132 0.362010611 0.571254503 0.454525067
## 73 74 75 76 77 78
## 0.654534606 0.956698153 0.924937603 0.802896314 0.982634576 1.378262422
## 79 80 81 82 83 84
## 1.807038228 1.581280092 1.395405579 0.992030019 1.216424096 1.047661757
## 85 86 87 88 89 90
## 1.278679605 0.726198923 0.601657287 0.344861700 0.174968971 -0.150744724
## 91 92 93 94 95 96
## 0.314674818 0.068024020 0.825029557 0.716439430 0.346274113 0.549324351
## 97 98 99 100 101 102
## 0.667736988 0.841428067 0.690830431 0.706628165 0.640008480 0.857655665
## 103 104 105 106 107 108
## 0.443817988 -0.620852423 0.782301579 0.400309839 0.862209606 0.540264479
## 109 110 111 112 113 114
## 0.935535765 1.098149659 -0.448055580 1.045665826 0.884899448 0.992795000
## 115 116 117 118 119 120
## 0.725535486 0.863861034 -0.015592757 0.421754495 0.643680411 0.121095446
## 121 122 123 124 125 126
## 0.192444848 -0.428640652 0.587991404 1.317571670 0.630410289 1.030016778
## 127 128 129 130 131 132
## 0.638061548 0.853042507 0.175554177 0.408035589 -0.385823644 -0.341518980
## 133 134 135 136 137 138
## 0.064563721 -0.873256926 -0.863441094 0.336990101 0.551495098 0.164858545
## 139 140 141 142 143 144
## 0.144624688 -0.614578540 0.671125231 -0.756484243 0.329425517 -0.214051631
## 145 146 147 148 149 150
## 0.502312457 0.546617121 -0.069881095 0.038038256 0.010827720 -0.382068463
## 151 152 153 154 155 156
## -0.288709572 -0.430281939 -0.385977275 -0.658769107 -0.541451645 -0.208861649
## 157 158 159 160 161 162
## 0.009898374 0.053678818 0.545467696 0.589772360 -0.482069286 -0.324318278
## 163 164 165 166 167 168
## -0.825355062 -0.263190827 -0.211678219 0.454882239 0.434648382 -0.199400825
## 169 170 171 172 173 174
## -0.027422857 -0.073006213 -0.010906411 -0.631366195 0.403108800 -0.898594398
## 175 176 177 178 179 180
## -1.520465388 -1.488680646 -1.585875608 -0.841148672 -0.733545036 -0.376191059
## 181 182 183 184 185 186
## 0.534298671 -0.087572319 0.164206090 -0.021450911 -1.104487756 -1.484003685
## 187 188 189 190 191 192
## -1.160780251 -0.691958622 -1.584119942 -1.844298293 -0.319388955 -0.501017433
## 193 194 195 196 197 198
## -0.075298339 -0.695566906 -1.264062160 -1.885933150 -0.803682692 -0.696257483
## 199 200 201 202 203 204
## -0.338376949 -0.408069614 -0.001145133 0.399633113 0.045903040 0.031020060
## 205 206 207 208 209 210
## -0.058575103 0.091698561 -0.022846332 0.020627883 0.269372440 0.138087858
## 211 212 213 214 215 216
## -0.073645921 -0.171275771 -0.351099196 0.136452850 -0.026460611 0.108626959
## 217 218 219 220 221 222
## 0.102108428 0.116281506 0.009686828 -0.280233188 0.048205423 -0.098274364
## 223 224 225 226 227 228
## 0.292856395 0.344645698 -0.090399456 -0.031073738 -0.055136671 -0.062179566
## 229 230 231 232 233 234
## -0.246194888 0.252092698 0.850831660 1.237670317 1.143743181 1.619840026
## 235 236 237 238 239 240
## 0.767348523 0.195591282 -0.231748279 0.005819147 0.745751734 0.687074491
## 241 242 243 244 245 246
## 1.359181503 0.605556514 0.413252689 -0.464306089 -0.960536780 0.294457612
## 247 248 249 250 251 252
## 0.012906746 -0.025883720 0.129434422 -0.224335611 0.042170231 0.406827927
## 253 254 255 256 257 258
## 0.270410106 0.117429426 -0.063906977 0.279615235 0.017803048 0.108054453
## 259 260 261 262 263 264
## 0.074863383 -0.049892035 -0.120705750 -0.072631289 -0.585800727 -0.469975543
## 265 266 267 268 269 270
## -0.720280463 -0.711112658 -0.728718820 -0.901676184 -1.050820970 -0.510362668
## 271 272 273 274 275 276
## -0.713126053 -1.280942318 -0.549380611 -0.567964221 -1.032067459 -0.655967313
## 277 278 279 280 281 282
## -0.623423051 -0.343770228 -0.427801767 -0.221350798 -0.464952907 -0.413393550
## 283 284 285 286 287 288
## -0.248467117 -0.147322908 -0.609797569 -0.874112889 -0.643772004 -0.444892033
## 289 290 291 292 293 294
## -1.944570370 -1.745399112 -1.749299537 -0.550808050 -1.418777491 -1.309182436
## 295 296 297 298 299 300
## -1.383076828 -1.022143134 -1.784001214 -1.131698130 -1.515964517 -1.451359863
## 301 302 303 304 305 306
## -1.549982710 -0.906686639 -1.223174104 -1.843346374 -0.979941375 -0.622732221
## 307 308 309 310 311 312
## 0.282213021 0.705465634 -0.231885528 -0.329258941 -0.138082096 0.130845738
## 313 314 315 316 317 318
## 0.462300073 -0.984404811 -0.647165072 -0.535054591 -0.405729946 -0.569523190
## 319 320 321 322 323 324
## -1.136348496 -0.698704457 -0.519517315 -0.984972619 -0.913278314 -0.842496058
## 325 326 327 328 329 330
## -1.931486426 -1.366976761 -0.396259062 0.210458594 -0.024744834 -0.208430383
## 331 332 333 334 335 336
## -0.563807295 -0.372795437 -0.475574344 -0.468552160 -0.035811463 -0.230524520
## 337 338 339 340 341 342
## 0.103203702 0.545222115 1.790948541 0.015468148 0.630274318 -0.378547375
## 343 344 345 346 347 348
## -0.360453450 -0.111905729 -0.549410048 -0.046702037 0.081118036 0.247193439
## 349 350 351 352 353 354
## 0.209422320 0.448524617 0.295296776 0.870686488 0.855363700 0.093149545
## 355 356 357 358 359 360
## -0.392268395 0.615982736 1.282396486 1.380177482 1.391941158 1.332181455
## 361 362 363 364 365 366
## 0.670250267 0.447404596 0.874816000 1.394506394 1.333724322 1.056803484
## 367 368 369 370 371 372
## 1.100546218 1.080636225 0.878085006 0.855951883 1.129774860 1.070554033
## 373 374 375 376 377 378
## 1.074192757 1.115652791 1.317805979 0.942873396 0.819657014 1.271029277
## 379 380 381 382 383 384
## 1.654219973 1.647530803 1.562742180 0.385583014 0.090231408 0.319106254
## 385 386 387 388 389 390
## 0.876061566 0.634780692 0.405024148 0.506976088 0.625122014 0.159180842
## 391 392 393 394 395 396
## 0.503795194 0.759402681 0.622038863 0.549350712 0.432401384 0.304195068
## 397 398 399 400 401 402
## -0.199656419 -0.166990674 -0.040097793 0.007171815 -0.311540737 -0.126567776
## 403 404 405 406 407 408
## 0.034336104 -0.713011779 0.009769598 -0.166971027 -0.310266644 -0.262247702
## 409 410 411 412 413 414
## -0.230346777 -0.250946422 -0.881167195 -0.219000473 -0.453105932 -0.567549918
## 415 416 417 418 419 420
## -0.541585696 -0.316158251 -0.644442267 -1.157060992 -0.944130870 -0.714249650
## 421 422 423 424 425 426
## -1.410037624 -1.441554786 -0.503370230 -1.015603107 -0.676855271 -0.478689460
## 427 428 429 430 431 432
## -0.309432861 -1.279358741 -0.795123629 -0.774958278 -0.870051628 -0.460562987
## 433 434 435 436 437 438
## 0.064269616 -0.557601374 -0.527957560 -0.496625530 -0.384213673 -0.086650305
## 439 440 441 442 443 444
## 0.315711420 1.196303375 -0.054176275 -0.558966810 -0.547926651 -1.123159358
## 445 446 447 448 449 450
## -0.633630321 -0.288301903 0.161797143 -0.520698469 -0.970158721 -1.018230265
## 451 452 453 454 455 456
## -1.474917212 -1.241433145 -0.840823567 -0.655920105 -0.754542951 -1.509717883
## 457 458 459 460 461 462
## -1.019416515 -0.787322851 -1.481948875 -1.136738003 -0.691139116 -0.581544061
## 463 464 465 466 467 468
## -0.620179678 0.013573898 -1.116517831 -1.380717737 -1.685965964 -1.641661300
## 469 470 471 472 473 474
## -1.080081121 -0.962784799 -1.336842529 -1.538708273 -2.005426655 -0.421991549
## 475 476 477 478 479 480
## -1.609992393 -0.910107543 -0.866649761 -0.693356531 -0.848838245 -0.388398991
## 481 482 483 484 485 486
## -1.329900388 -0.994179727 -0.595860390 -0.305015606 -0.186189695 -0.137481165
## 487 488
## 0.072232710 -0.307177484
mod_dl13_hanover <- dlm(log_mean_new_cases ~ log_viral_gene,
data = full_cases_wastewater_weather_data_hanover_train,
q=13)
summary(mod_dl13_hanover)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9269 -0.5394 0.0253 0.5566 1.5463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.266744 0.321639 -25.702 <2e-16 ***
## log_viral_gene.t 0.162195 0.059105 2.744 0.0063 **
## log_viral_gene.1 0.036405 0.080869 0.450 0.6528
## log_viral_gene.2 -0.009323 0.080998 -0.115 0.9084
## log_viral_gene.3 0.057573 0.082325 0.699 0.4847
## log_viral_gene.4 0.108674 0.082369 1.319 0.1877
## log_viral_gene.5 0.010806 0.083125 0.130 0.8966
## log_viral_gene.6 0.021985 0.083091 0.265 0.7914
## log_viral_gene.7 0.019192 0.083111 0.231 0.8175
## log_viral_gene.8 0.090591 0.083330 1.087 0.2775
## log_viral_gene.9 -0.044655 0.082663 -0.540 0.5893
## log_viral_gene.10 0.021492 0.082655 0.260 0.7950
## log_viral_gene.11 0.083382 0.081444 1.024 0.3065
## log_viral_gene.12 0.015224 0.081440 0.187 0.8518
## log_viral_gene.13 0.016637 0.059523 0.280 0.7800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7452 on 462 degrees of freedom
## Multiple R-squared: 0.6203, Adjusted R-squared: 0.6088
## F-statistic: 53.91 on 14 and 462 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1089.883 1156.563
f_dl13_hanover <- forecast(mod_dl13_hanover,
x= t(full_cases_wastewater_weather_data_hanover_test[,7]),
h=14)
rmse(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl13_hanover$forecasts)
## [1] 0.5809196
mae(full_cases_wastewater_weather_data_hanover_test$log_mean_new_cases,
f_dl13_hanover$forecasts)
## [1] 0.4512274
checkresiduals(mod_dl13_hanover)
## 1 2 3 4 5 6
## 0.774788470 0.744986890 0.310267632 0.377049317 0.472122652 0.615842951
## 7 8 9 10 11 12
## 0.711424358 0.783185854 0.848608783 0.589622348 0.492853798 0.450875717
## 13 14 15 16 17 18
## 0.240777065 1.122294650 0.582931274 0.909985345 0.218732044 0.690836860
## 19 20 21 22 23 24
## 0.602675907 0.523796450 0.874284496 1.161813927 1.082547651 0.659340026
## 25 26 27 28 29 30
## 0.585210885 0.784155229 0.778580745 0.962826231 0.682649131 0.374406556
## 31 32 33 34 35 36
## 0.589759882 0.439354491 0.334767929 0.026509367 0.292449497 -0.154979209
## 37 38 39 40 41 42
## 0.279393601 0.125351453 -0.192808619 0.247397637 -0.045946718 0.366809223
## 43 44 45 46 47 48
## 0.577278030 0.679749794 0.447464955 0.353164730 0.523188470 0.728504280
## 49 50 51 52 53 54
## 1.018313373 0.968222238 0.830446865 0.566907429 1.406217062 1.377208508
## 55 56 57 58 59 60
## 1.187276230 0.830754896 1.284826430 0.972990986 0.845031305 1.020313999
## 61 62 63 64 65 66
## 0.865147233 1.007257915 1.145776343 1.261468134 1.116165987 0.988965763
## 67 68 69 70 71 72
## 1.392313541 1.393580356 1.286913304 1.250360786 1.127511846 1.362147560
## 73 74 75 76 77 78
## 1.114204166 1.436643633 0.823277829 0.803704180 0.555877495 0.872252402
## 79 80 81 82 83 84
## 0.493581707 0.619129675 0.347525367 0.763454761 0.638586080 0.270055232
## 85 86 87 88 89 90
## 0.546519601 0.689464465 0.769864796 0.672985955 0.638360305 0.546502662
## 91 92 93 94 95 96
## 0.877918177 0.480613375 -0.533594559 0.837080099 0.441750729 0.798189632
## 97 98 99 100 101 102
## 0.471521585 0.927905155 1.150551679 -0.365891073 1.095341161 0.957338871
## 103 104 105 106 107 108
## 0.977303104 0.726425984 0.923026454 0.188857256 0.641405764 0.832204328
## 109 110 111 112 113 114
## 0.296711253 0.423878760 -0.473482685 0.588434857 0.709145143 0.175470993
## 115 116 117 118 119 120
## 0.865882057 0.421420407 0.936374177 0.301665362 0.620018548 0.011011473
## 121 122 123 124 125 126
## 0.051723845 0.531600047 -0.485780831 -0.380418816 0.628788477 0.716913612
## 127 128 129 130 131 132
## 0.071841449 0.105413905 -0.546628972 0.676526049 -0.497096788 0.383093497
## 133 134 135 136 137 138
## -0.100305661 0.176308887 0.335366733 -0.049110705 -0.009301489 0.068129770
## 139 140 141 142 143 144
## -0.195381071 -0.079586626 0.210419940 0.196961696 -0.275896594 -0.143128130
## 145 146 147 148 149 150
## -0.180003267 0.002847022 0.055304027 0.556564247 0.640825883 -0.371840798
## 151 152 153 154 155 156
## -0.187518832 -0.324557289 0.002303091 0.087227432 0.350182006 0.438701013
## 157 158 159 160 161 162
## -0.029045593 -0.004834965 0.094553008 0.101771040 -0.268501898 0.614349187
## 163 164 165 166 167 168
## 0.061767300 -0.586762593 -0.798908356 -0.888205260 -0.101138684 -0.369639854
## 169 170 171 172 173 174
## -0.196634633 -0.046150393 -0.547514341 0.014461102 -0.266992717 -0.708934597
## 175 176 177 178 179 180
## -1.008430549 -0.720543527 0.053047615 -0.922935279 -1.247687905 0.151235684
## 181 182 183 184 185 186
## -0.202870074 0.233058608 -0.627941961 -1.028431693 -1.722841186 -0.707015985
## 187 188 189 190 191 192
## -0.560779092 0.032993665 -0.148814259 0.194153377 0.459734866 0.123055279
## 193 194 195 196 197 198
## 0.128923127 -0.061869293 0.206754363 0.081914160 0.045076967 0.318980533
## 199 200 201 202 203 204
## 0.162548758 0.039540998 -0.086887354 -0.018984925 0.372282812 0.081729720
## 205 206 207 208 209 210
## 0.124475531 0.110667272 0.157256726 -0.028630634 -0.160968272 0.095037633
## 211 212 213 214 215 216
## -0.132578852 0.139858254 0.194872707 -0.097449007 -0.087710852 0.200711310
## 217 218 219 220 221 222
## 0.042721744 -0.236465873 -0.014152501 0.614388266 0.963617285 0.845120391
## 223 224 225 226 227 228
## 0.987447648 0.399712347 -0.082579022 0.025301040 0.178778739 0.541528949
## 229 230 231 232 233 234
## 0.695648070 0.531946918 0.113037886 0.079329676 -0.068881612 -0.647177877
## 235 236 237 238 239 240
## 0.227123054 0.151337728 -0.157121913 -0.046052246 -0.323325870 -0.122273943
## 241 242 243 244 245 246
## 0.290843118 0.068676742 -0.079275514 -0.257593745 0.010125406 -0.154942970
## 247 248 249 250 251 252
## -0.337275150 -0.301100832 -0.279527459 -0.329204608 -0.253721288 -0.669781303
## 253 254 255 256 257 258
## -0.512419296 -0.540599736 -0.567146843 -0.650645701 -0.797176479 -1.047242222
## 259 260 261 262 263 264
## -0.539414751 -0.783869264 -1.386394202 -0.648836280 -0.696045039 -1.136111557
## 265 266 267 268 269 270
## -0.732849422 -0.830877595 -0.480399593 -0.948837092 -0.654954675 -0.730548209
## 271 272 273 274 275 276
## -0.667938010 -0.446138390 -0.313021373 -0.683641094 -0.952095913 -0.707798809
## 277 278 279 280 281 282
## -0.463436606 -1.926916936 -1.821256891 -1.790765283 -0.582371330 -1.367892111
## 283 284 285 286 287 288
## -1.267663332 -1.406530741 -0.996849874 -1.853436514 -1.168182165 -1.525007463
## 289 290 291 292 293 294
## -1.374388115 -1.478453920 -0.900224229 -1.185043816 -1.878780313 -1.302689498
## 295 296 297 298 299 300
## -0.836590365 -0.785759143 -0.176223174 -0.804897533 -0.839923028 -0.630459620
## 301 302 303 304 305 306
## -0.067476028 0.504647131 -0.396727934 -0.126155303 0.008627863 0.172520522
## 307 308 309 310 311 312
## 0.091571689 -0.474259249 -0.311014011 0.190630195 -0.375910125 -0.634555994
## 313 314 315 316 317 318
## -0.620097844 -1.838607224 -1.278530598 -0.377264760 0.282523383 0.029353404
## 319 320 321 322 323 324
## -0.216191038 -0.548643509 -0.357213877 -0.469242105 -0.457389049 -0.021692691
## 325 326 327 328 329 330
## -0.212770581 -0.256569655 0.301780910 0.459724999 -0.710959005 0.199726781
## 331 332 333 334 335 336
## 0.383602305 0.248337722 0.135864346 0.015516911 0.311666401 0.414498575
## 337 338 339 340 341 342
## 0.507365101 0.684646531 0.902496977 0.419097459 0.917110623 0.891755853
## 343 344 345 346 347 348
## 0.116473068 -0.402330123 0.616103534 1.274606872 1.426607373 1.414402646
## 349 350 351 352 353 354
## 1.546341994 0.840501804 0.518584663 0.959608108 1.457521203 1.437402473
## 355 356 357 358 359 360
## 1.085428745 1.372449000 1.278043644 0.926514617 0.869893804 1.119305861
## 361 362 363 364 365 366
## 1.050880532 0.990437398 1.095378230 1.228622730 0.792698002 0.533158658
## 367 368 369 370 371 372
## 0.997300573 1.369735844 1.387962651 1.148842028 0.111342116 -0.123421763
## 373 374 375 376 377 378
## 0.405276927 0.919350649 0.574777456 0.412535968 0.401749220 0.412713982
## 379 380 381 382 383 384
## -0.048624621 0.044425483 0.358254406 0.220227677 0.184274065 -0.024578248
## 385 386 387 388 389 390
## -0.083486178 -0.443006462 -0.360932533 -0.216488431 -0.134808479 -0.393002109
## 391 392 393 394 395 396
## -0.284912955 -0.217152201 -0.910757658 -0.468644185 -0.576666118 -0.694444883
## 397 398 399 400 401 402
## -0.583986570 -0.742317313 -0.675351742 -1.118187567 -0.413250045 -0.618778857
## 403 404 405 406 407 408
## -0.714311475 -0.583969108 -0.527272818 -0.873728486 -1.281744832 -1.193543856
## 409 410 411 412 413 414
## -0.912483256 -1.596773430 -1.557833890 -0.726948228 -1.251785632 -0.770482170
## 415 416 417 418 419 420
## -0.724623437 -0.496638591 -1.294718536 -0.778456499 -0.546260259 -0.855888835
## 421 422 423 424 425 426
## -0.400622518 -0.441294023 -0.949167083 -0.692229365 -0.686973035 -0.513527566
## 427 428 429 430 431 432
## -0.283084888 0.267373262 0.792611920 -0.371144364 -0.405178932 -0.402864782
## 433 434 435 436 437 438
## -0.303682514 -0.066089440 0.163773350 0.149197364 -0.476710102 -0.549930349
## 439 440 441 442 443 444
## -0.823372487 -0.566266857 -0.541877202 -0.405083165 -0.529610829 -0.639083914
## 445 446 447 448 449 450
## -1.111222926 -0.808917389 -0.051019902 -0.998746713 -0.879704351 -0.906377555
## 451 452 453 454 455 456
## -0.763763607 -0.464301498 0.025522948 -0.530598354 -0.895526523 -1.395853208
## 457 458 459 460 461 462
## -1.432745566 -0.899089993 -0.720543601 -1.212967195 -1.353783950 -1.852105881
## 463 464 465 466 467 468
## -0.408947493 -1.613523935 -0.935683923 -0.845425136 -0.667414353 -0.663817552
## 469 470 471 472 473 474
## -0.279279232 -1.268011300 -1.045359280 -0.634008213 -0.429224601 -0.315341873
## 475 476 477
## -0.563285865 -0.200609987 -0.498041216
wake_mod_dl14_res <- ggAcf(residuals(mod_dl14)) +
theme_bw(base_size = 15) + ggtitle("")
## 1 2 3 4 5 6
## -0.151770801 -0.160174319 -0.006891305 0.012071577 -0.068008232 0.122592200
## 7 8 9 10 11 12
## 0.015847908 -0.178071430 0.214099747 -0.006353717 -0.012215233 -0.298606308
## 13 14 15 16 17 18
## 0.354637808 0.025646543 -0.260584528 0.180020051 0.013853802 0.158328818
## 19 20 21 22 23 24
## 0.278353673 0.210017083 -0.078877295 -0.348110739 0.055222675 -0.110048519
## 25 26 27 28 29 30
## -0.061257221 -0.044888949 -0.037927120 -0.391780768 -0.357219577 -0.325654025
## 31 32 33 34 35 36
## -0.173423164 -0.161965045 -0.331116892 -0.070850976 -0.327220624 -0.077795680
## 37 38 39 40 41 42
## -0.192371480 -0.199630447 -0.499721719 -0.339997397 -0.186092416 -0.112659390
## 43 44 45 46 47 48
## 0.046153616 -0.065795631 -0.027007380 0.272730134 0.385322871 0.284586325
## 49 50 51 52 53 54
## 0.408328451 0.418240641 0.607870058 0.227049609 0.244602361 0.437649300
## 55 56 57 58 59 60
## 0.361156912 0.546368097 0.755777260 0.480700608 0.637950909 0.761534885
## 61 62 63 64 65 66
## 0.367490147 0.299815161 0.125096013 0.327222264 0.264879971 0.021003598
## 67 68 69 70 71 72
## -0.314816009 -0.158956628 -0.277862458 -0.061712910 0.215764953 -0.300915457
## 73 74 75 76 77 78
## 0.034125718 0.320742606 -0.013196360 -0.464188949 -0.230510455 0.398974451
## 79 80 81 82 83 84
## 0.678452605 0.333376179 0.221424191 0.490438548 0.447209701 0.534268079
## 85 86 87 88 89 90
## 0.709815225 0.119640883 0.504932076 0.261929540 0.246888146 0.194527175
## 91 92 93 94 95 96
## 0.178860328 0.206730858 0.252978892 0.005364263 0.074426266 0.216287910
## 97 98 99 100 101 102
## 0.232817539 0.472290377 0.614895530 0.447324577 0.424654756 0.445229243
## 103 104 105 106 107 108
## 0.310757531 0.385827965 0.093229086 0.539775588 0.138891230 0.432588068
## 109 110 111 112 113 114
## 0.280276822 0.381751416 0.606126225 0.676981509 0.861906417 0.755161556
## 115 116 117 118 119 120
## 0.905947690 1.096363380 0.879085200 0.986306869 0.824226121 0.934572457
## 121 122 123 124 125 126
## 0.910965863 1.303534614 0.903807919 0.996189016 0.642240600 0.893461200
## 127 128 129 130 131 132
## 1.098934200 0.717405303 0.966141121 0.347449470 0.226289563 0.190708147
## 133 134 135 136 137 138
## 0.279640583 0.546293239 -0.972154654 -0.343724632 -1.439011674 -0.468140737
## 139 140 141 142 143 144
## -0.038232381 0.061734132 0.289038977 -0.648272094 -0.593070505 -0.507174123
## 145 146 147 148 149 150
## -0.433670957 -0.830026838 -0.441469781 -0.549782252 -0.114253460 -0.211018737
## 151 152 153 154 155 156
## -0.002542970 -0.025310874 0.152103161 0.021355744 -0.153498703 -0.488846098
## 157 158 159 160 161 162
## -0.292301718 -0.917386352 -0.565715895 -0.853973793 -0.323561354 -0.431294276
## 163 164 165 166 167 168
## -0.624386866 -0.973825825 -0.870499160 -0.656768083 -0.559515570 -0.817463012
## 169 170 171 172 173 174
## -2.439120965 -1.011462182 -0.885873005 -0.813675933 -0.818385289 -0.226150827
## 175 176 177 178 179 180
## -0.307792930 -0.183935955 -0.076929703 -0.215211957 -0.557805408 0.148763847
## 181 182 183 184 185 186
## -0.101680887 -0.117617739 0.143736499 0.020394433 0.337207754 0.045956078
## 187 188 189 190 191 192
## 0.332593271 0.256071911 0.247573241 0.629550849 0.509287247 0.192702377
## 193 194 195 196 197 198
## 0.071292443 0.565404648 0.436179259 0.301658228 0.232234299 0.393091647
## 199 200 201 202 203 204
## 0.079781736 0.118662310 0.338854035 0.045047977 0.088193667 0.237000094
## 205 206 207 208 209 210
## 0.238516762 0.086160984 0.041897754 0.315808665 0.229016112 0.125181519
## 211 212 213 214 215 216
## 0.151657938 0.337117793 0.162295906 0.296032161 0.514344361 0.468765657
## 217 218 219 220 221 222
## 0.496941398 0.346308667 0.712701681 0.474850754 0.594063627 0.649302975
## 223 224 225 226 227 228
## 0.655152141 1.093468567 0.364177085 0.531892550 0.388969558 0.627855968
## 229 230 231 232 233 234
## 0.558245460 0.300468018 0.212893475 -0.522911391 -1.841610748 -0.155285556
## 235 236 237 238 239 240
## -0.508681021 -0.579301985 -0.268928725 -0.189132236 -0.548010627 -0.388553086
## 241 242 243 244 245 246
## -0.570005532 -0.318321249 -0.476077039 -0.551777154 -0.429298466 -0.723291715
## 247 248 249 250 251 252
## -0.497671782 -0.548269407 -0.597052392 -0.719545452 -0.418849460 -0.672944848
## 253 254 255 256 257 258
## -1.010622705 -0.327623496 -0.575844083 -0.556350035 -0.523688877 -0.519657389
## 259 260 261 262 263 264
## -0.268375536 -0.803853303 -0.610959894 -0.710925756 -0.510139753 -0.539475414
## 265 266 267 268 269 270
## 0.234843138 -0.608050746 -0.027640151 -0.374300241 -0.212675738 0.334159885
## 271 272 273 274 275 276
## 0.076729409 -0.369232372 -0.523525111 -1.050303551 -0.205229336 -0.283065176
## 277 278 279 280 281 282
## -0.125127059 -2.606668860 -1.887651121 0.137770559 -0.614603483 -0.393221520
## 283 284 285 286 287 288
## -0.027077421 -0.031360472 -0.227814319 -0.047417728 -0.020386512 -0.539459137
## 289 290 291 292 293 294
## -0.383600678 -0.422027824 -0.323895183 -0.631557439 -0.365336871 -0.369111965
## 295 296 297 298 299 300
## -0.035236118 -0.547808614 -1.315971321 -0.329583472 -0.750814942 -0.091505927
## 301 302 303 304 305 306
## -0.482518346 -0.259376639 -0.122673196 -0.359898283 0.033848038 0.335394645
## 307 308 309 310 311 312
## 0.524354738 0.927982380 0.780829953 0.418791558 0.186413545 0.182083536
## 313 314 315 316 317 318
## -0.373833890 0.127315760 0.390806471 0.138672724 0.573963506 0.458075879
## 319 320 321 322 323 324
## 0.839090143 0.739579581 0.686325113 0.675773388 0.831578480 0.341718760
## 325 326 327 328 329 330
## 0.290288367 0.168494837 -0.144210596 0.144610634 0.048771048 0.254732871
## 331 332 333 334 335 336
## 0.042042209 -0.225549990 -0.236827529 -0.176274543 -0.038612283 0.312138062
## 337 338 339 340 341 342
## 0.238171523 0.136415396 0.276010470 0.540565247 0.882857955 0.296840260
## 343 344 345 346 347 348
## -0.137283545 1.023863671 1.419062128 1.570806375 1.494699904 1.448212011
## 349 350 351 352 353 354
## 0.970092989 1.044901228 1.096022120 1.360122567 1.710005296 1.493208650
## 355 356 357 358 359 360
## 1.339123639 1.201445618 1.143456231 0.512135705 1.140535149 0.884675146
## 361 362 363 364 365 366
## 1.011324742 0.652221238 0.549047199 0.263673674 -1.126485235 -0.316701781
## 367 368 369 370 371 372
## 0.717132716 0.585472735 0.438581794 -0.771989008 -1.290460799 -0.108444124
## 373 374 375 376 377 378
## 0.646418665 -0.028111462 0.033091842 -0.250391953 -0.174030337 -0.676824629
## 379 380 381 382 383 384
## -0.411439361 0.179887039 0.042274760 -0.135621401 -0.035189170 0.120473964
## 385 386 387 388 389 390
## 0.082071971 0.127908668 -0.062952369 -0.241917541 0.150867958 -0.306590869
## 391 392 393 394 395 396
## -0.351989173 -0.248284189 -0.229355365 0.066177156 -0.236726148 -0.360486102
## 397 398 399 400 401 402
## -0.117368445 -0.335625206 -0.432859367 -0.091015252 -0.352087825 -0.416276302
## 403 404 405 406 407 408
## -0.549777331 -0.545873481 -0.383512457 -0.921388416 -0.504774156 -0.748695127
## 409 410 411 412 413 414
## -0.782727437 -0.560935127 -0.008560035 -0.664322358 -0.408533211 -0.069387305
## 415 416 417 418 419 420
## -0.273464059 -0.132595114 -0.594053109 0.066738616 -0.340858730 -0.257368374
## 421 422 423 424 425 426
## -0.414811767 -0.060867515 -0.585942332 -0.240590621 -0.088740505 -0.410675912
## 427 428 429 430 431 432
## -0.374591384 0.066396452 -0.154500894 -0.535570467 -0.453401557 -0.172807709
## 433 434 435 436 437 438
## -0.458378403 -0.781191169 -0.629485851 -0.904539340 -0.437470823 -0.822157694
## 439 440 441 442 443 444
## -0.606324690 -0.105332875 -0.463414756 -0.232166849 -0.367055143 -0.600122567
## 445 446 447 448 449 450
## -0.257259980 -0.453475603 -0.286459956 -0.056093756 -0.301833108 -0.395416052
## 451 452 453 454 455 456
## 0.025042902 0.097045855 0.140881259 -0.036051822 0.280518057 0.096068539
## 457 458 459 460 461 462
## -0.029904984 0.081309895 -0.180521132 -0.067073493 0.033031739 0.025108241
## 463 464 465 466 467 468
## 0.216817157 -0.279499964 -0.066774088 -0.114070837 -0.288768122 -0.131827100
## 469 470 471 472 473 474
## -0.147972310 -0.398907266 -0.195345702 -0.192634128 -0.193318660 0.072075552
## 475 476
## -0.107907378 0.190390635
meck_mod_dl14_res <- ggAcf(residuals(mod_dl14_meck)) +
theme_bw(base_size = 15) + ggtitle("")
## 1 2 3 4 5 6
## 0.083673414 0.203715871 0.108310564 0.045605367 0.110362522 0.393824828
## 7 8 9 10 11 12
## 0.283817235 0.228569589 -0.026232304 0.407629201 0.361447059 0.052547076
## 13 14 15 16 17 18
## 0.178001206 0.472462403 0.552468387 0.433889572 0.248862452 0.077375063
## 19 20 21 22 23 24
## 0.100255268 -0.155851852 0.383149327 0.144611745 -0.141688388 -0.114885685
## 25 26 27 28 29 30
## -0.305414029 -0.073615076 0.035925731 -0.252943021 -0.244670279 0.087310528
## 31 32 33 34 35 36
## -0.197463150 -0.414951938 -0.149099555 -0.381173178 0.105180877 -0.507462204
## 37 38 39 40 41 42
## -0.927093891 -0.222960778 -0.261467804 -0.278147642 -0.227185504 -0.378278193
## 43 44 45 46 47 48
## 0.159035080 -0.273853376 -0.092976634 -1.069741022 -0.948109530 -0.306405589
## 49 50 51 52 53 54
## -0.863064403 0.480081475 0.778805931 0.711123070 0.895631949 1.175119854
## 55 56 57 58 59 60
## 1.470857538 1.673620842 0.877213084 0.798740972 0.606666470 0.926610972
## 61 62 63 64 65 66
## 0.822451538 1.109450802 1.085787869 1.182070764 0.857658253 0.731467011
## 67 68 69 70 71 72
## 0.488390679 0.108432878 0.324193401 0.536438611 0.288742072 -0.172080777
## 73 74 75 76 77 78
## 0.300727820 0.168724681 0.274726918 0.031480759 0.049598504 0.373607464
## 79 80 81 82 83 84
## -0.002866966 -0.108282393 -0.176879302 0.005139536 0.039720451 0.006671769
## 85 86 87 88 89 90
## 0.082309573 0.012106944 0.195568556 0.117092948 -0.226234898 0.304477535
## 91 92 93 94 95 96
## -0.389882718 0.613438625 0.412712740 0.057138967 0.352902740 0.008560608
## 97 98 99 100 101 102
## 0.278130924 0.602149876 0.430990641 0.419864616 0.032364319 -0.316782862
## 103 104 105 106 107 108
## 0.283565605 -0.175242847 -0.158905309 -0.037251591 -0.110680855 -0.362177583
## 109 110 111 112 113 114
## -0.254869641 -0.628388144 -0.436689816 -0.150006003 0.007474222 -0.479450536
## 115 116 117 118 119 120
## -0.311955557 -0.741149972 -0.227838354 -0.128741053 0.581673961 0.229427592
## 121 122 123 124 125 126
## 0.065854073 -0.227517218 -0.322209225 0.165986256 -0.351316573 -0.412853967
## 127 128 129 130 131 132
## 0.703709198 0.141136814 -0.637472279 0.209881186 0.749356210 0.590173817
## 133 134 135 136 137 138
## 0.642901903 0.368915261 0.176590063 1.292981938 0.296486825 -0.152654063
## 139 140 141 142 143 144
## -0.047852413 0.396782323 0.042512824 -0.140314907 -0.315514338 -0.152180505
## 145 146 147 148 149 150
## 0.139575873 -0.356172563 0.071344091 0.330071292 0.465744800 0.647180537
## 151 152 153 154 155 156
## -0.240704446 -0.433002635 -0.418524658 0.178443669 -0.202221510 -0.988534265
## 157 158 159 160 161 162
## -1.104346842 -0.378046737 -0.599136381 -1.160978629 -0.504870864 -0.218204950
## 163 164 165 166 167 168
## -0.997848618 -0.847337339 -0.970523182 -0.058223360 -0.066176988 -0.276425474
## 169 170 171 172 173 174
## -0.394131347 -0.348757251 -0.486810964 -0.184599029 0.181121759 0.341363720
## 175 176 177 178 179 180
## 0.597635822 0.554918616 -0.046330493 0.344939888 0.135983889 0.157789623
## 181 182 183 184 185 186
## 0.172392220 0.035975707 0.697702454 0.251142866 0.314330712 0.462649289
## 187 188 189 190 191 192
## 0.554286428 0.404283953 0.432232194 0.454116679 0.405956061 0.254142897
## 193 194 195 196 197 198
## 0.506486369 0.639235343 0.173128478 0.317428907 0.357183148 0.097078915
## 199 200 201 202 203 204
## -0.145247699 -0.115962461 0.152087391 -0.005357401 -0.211596058 -0.050151630
## 205 206 207 208 209 210
## 0.056863765 0.037783605 0.240534616 0.288189768 0.043790436 -0.240101494
## 211 212 213 214 215 216
## -0.157707365 -0.056896908 0.125865046 0.109479264 0.211576331 0.394874826
## 217 218 219 220 221 222
## 0.324116687 0.368418890 0.408429453 0.104188411 0.054861850 0.144561498
## 223 224 225 226 227 228
## 0.321135690 0.158932473 0.006441350 0.161730015 -0.014472257 -0.247536562
## 229 230 231 232 233 234
## -0.058038082 -0.174460627 -0.280441817 -0.218221623 -1.236400020 -0.303947449
## 235 236 237 238 239 240
## -0.212385134 -0.267329530 -0.187324705 -0.174693433 -0.379732549 -0.198600813
## 241 242 243 244 245 246
## -0.355265131 -0.588452008 -0.407572550 -0.358375338 -0.520762780 -0.680479784
## 247 248 249 250 251 252
## -0.425806851 -0.490049514 -0.671583984 -0.429451793 -0.435406359 -0.394451973
## 253 254 255 256 257 258
## -0.648419830 -0.339791705 -0.554080852 -0.044116526 -0.192096899 -0.179573145
## 259 260 261 262 263 264
## -0.367558237 -0.675288139 -0.331304639 -0.313166651 -0.728111349 -0.611805831
## 265 266 267 268 269 270
## -0.168956313 -0.458199417 -0.367018295 -0.211525045 -0.361337641 -0.143816302
## 271 272 273 274 275 276
## -0.244640382 -0.077397245 -0.029399448 -0.277802980 -0.267612959 -0.450998155
## 277 278 279 280 281 282
## -0.408262589 -1.499252712 -1.129477922 -0.112450865 0.039643067 -0.324413390
## 283 284 285 286 287 288
## -0.290525830 -0.041874533 -0.459955189 0.027960488 0.297860449 -0.112198979
## 289 290 291 292 293 294
## -0.267310416 -0.273467438 -0.776781816 -0.342723799 -0.185990398 -0.008966314
## 295 296 297 298 299 300
## -0.075112821 -0.005481946 -0.272122270 -0.122574727 -0.174129075 -0.065889338
## 301 302 303 304 305 306
## 0.047714726 0.298739868 -0.025017908 0.289811610 0.217793082 0.239615121
## 307 308 309 310 311 312
## 0.239571458 0.414151066 0.257634125 0.204833149 0.506767865 0.406909890
## 313 314 315 316 317 318
## -0.057258669 0.482213312 1.231821470 0.721636017 0.728648391 0.500368238
## 319 320 321 322 323 324
## 0.731164422 0.642727538 0.907181007 0.502277235 0.234604449 0.227290927
## 325 326 327 328 329 330
## 0.041763187 0.034718302 -0.090580190 0.144835121 0.191011942 0.117674808
## 331 332 333 334 335 336
## 0.296869566 0.125979818 0.381965504 0.525056634 0.443657128 0.454052683
## 337 338 339 340 341 342
## 0.586118672 0.628964184 0.923735461 1.072776733 1.185790856 0.998244704
## 343 344 345 346 347 348
## 0.253340933 1.331491217 1.652599841 1.737726257 1.830308586 1.981473344
## 349 350 351 352 353 354
## 1.532152911 1.272594809 1.682241025 1.404727965 1.354108842 1.432703322
## 355 356 357 358 359 360
## 0.857938160 0.905015563 0.588338824 0.397328873 0.853828081 0.610746309
## 361 362 363 364 365 366
## 0.621299482 0.476321744 0.409339184 0.197701568 -1.422533507 -0.616534030
## 367 368 369 370 371 372
## 0.223464548 0.300899504 0.100463617 -0.048853561 -0.501220205 -0.265002792
## 373 374 375 376 377 378
## 0.038305076 -0.124335803 -0.181012347 -0.264522309 -0.295319384 -0.454387699
## 379 380 381 382 383 384
## -0.375987394 0.119548942 -0.173341685 0.010694421 -0.135396856 0.088129302
## 385 386 387 388 389 390
## -0.122878115 -0.224254237 0.491590967 0.390222335 0.413354790 0.507118521
## 391 392 393 394 395 396
## 0.390756165 0.224829384 -0.395754231 0.394496872 0.131855036 -0.010801313
## 397 398 399 400 401 402
## 0.093833413 0.137200493 0.081621831 0.060338738 0.480498679 0.507988234
## 403 404 405 406 407 408
## 0.272410677 0.368974209 0.515291904 -0.319724897 -1.206895697 -0.137937622
## 409 410 411 412 413 414
## -0.489106405 -0.636590369 -0.282526529 -0.618754014 -1.073271939 -0.120288440
## 415 416 417 418 419 420
## -0.796112808 -1.013106913 -0.995653753 -1.527820192 -0.975681290 -0.760436347
## 421 422 423 424 425 426
## -1.135932461 -1.105016648 -0.818919288 0.181468417 -0.490653826 -0.725625459
## 427 428 429 430 431 432
## -0.903965703 -0.619550178 -0.408564854 -0.701227412 -0.496222007 -0.290672830
## 433 434 435 436 437 438
## -0.547162448 -0.890290220 -0.228505158 -1.064244357 0.213677325 0.033515382
## 439 440 441 442 443 444
## -0.217047684 -0.711160301 -0.465666053 -0.649149701 -0.309713911 -0.370760781
## 445 446 447 448 449 450
## -0.226032639 -0.077406740 -0.409509028 -0.842848432 -0.124986960 0.201279365
## 451 452 453 454 455 456
## 0.119362479 0.250029094 -0.013946757 -0.695203647 -0.479920168 -1.362543319
## 457 458 459 460 461 462
## -0.437744273 -0.441604822 -0.580462180 -0.474034803 -0.742117255 -0.958541231
## 463 464 465 466 467 468
## -0.784336697 -0.334692619 -0.592994945 -0.270884088 -0.603632500 -0.728979911
## 469 470 471 472 473 474
## -0.588428646 -0.612960962 -0.473513648 -0.557718658 -0.430461009 -0.501864842
## 475 476
## -0.389870632 -0.205309993
hanover_mod_dl14_res <- ggAcf(residuals(mod_dl14_hanover)) +
theme_bw(base_size = 15) + ggtitle("")
## 1 2 3 4 5 6
## 0.747671788 0.307641508 0.378269471 0.473802219 0.619452137 0.711640715
## 7 8 9 10 11 12
## 0.784764229 0.851181386 0.587009244 0.494110837 0.452150818 0.244520123
## 13 14 15 16 17 18
## 1.122428761 0.583604437 0.912896054 0.215617235 0.691798693 0.600442412
## 19 20 21 22 23 24
## 0.524673916 0.873202989 1.163039524 1.087161000 0.647565642 0.586902041
## 25 26 27 28 29 30
## 0.787283320 0.752887310 0.961409396 0.688481219 0.380161119 0.573329284
## 31 32 33 34 35 36
## 0.443081736 0.358261805 0.027539317 0.293750417 -0.150229915 0.271321532
## 37 38 39 40 41 42
## 0.122643563 -0.191472098 0.266413213 -0.044373382 0.366898659 0.576119311
## 43 44 45 46 47 48
## 0.673770853 0.442499814 0.353702994 0.518073738 0.721501191 1.016752586
## 49 50 51 52 53 54
## 0.968241689 0.797826891 0.564507013 1.403061846 1.371784098 1.189120163
## 55 56 57 58 59 60
## 0.831064425 1.273177601 0.966582768 0.844717559 1.023075623 0.807142418
## 61 62 63 64 65 66
## 1.018402414 1.150247042 1.277706262 1.143776243 0.986930140 1.396903771
## 67 68 69 70 71 72
## 1.453890134 1.287967088 1.252050855 1.127398886 1.351576932 1.109953607
## 73 74 75 76 77 78
## 1.439402548 0.826177275 0.798481506 0.559887259 0.878814915 0.460054856
## 79 80 81 82 83 84
## 0.618189988 0.354178901 0.800934551 0.644800810 0.272745138 0.556436014
## 85 86 87 88 89 90
## 0.698699805 0.765819983 0.676171855 0.678981448 0.541217929 0.878639863
## 91 92 93 94 95 96
## 0.480107399 -0.567074083 0.835251043 0.443114773 0.798032497 0.475458293
## 97 98 99 100 101 102
## 0.929089500 1.151674303 -0.365146410 1.092744210 0.958868595 0.975938609
## 103 104 105 106 107 108
## 0.727230555 0.924896703 0.191074765 0.630066217 0.830326618 0.300237101
## 109 110 111 112 113 114
## 0.431653877 -0.470709044 0.587993289 0.713496419 0.170954979 0.864112086
## 115 116 117 118 119 120
## 0.419857150 0.941106815 0.304678257 0.619942958 0.000665306 0.049049003
## 121 122 123 124 125 126
## 0.532278958 -0.483855497 -0.438958916 0.642657182 0.719306023 0.083623883
## 127 128 129 130 131 132
## 0.142308364 -0.547859467 0.679362968 -0.466719588 0.386998573 -0.101381340
## 133 134 135 136 137 138
## 0.172972328 0.335315478 -0.049409208 -0.011413372 0.034182159 -0.186190837
## 139 140 141 142 143 144
## -0.077516488 0.206178558 0.216607175 -0.276560341 -0.139998257 -0.212428313
## 145 146 147 148 149 150
## 0.010084704 0.058939187 0.568749793 0.651043913 -0.375174713 -0.182188461
## 151 152 153 154 155 156
## -0.276029586 -0.002888015 0.087513971 0.351314577 0.403895340 -0.027424995
## 157 158 159 160 161 162
## -0.004155429 0.089282066 0.116703756 -0.267717173 0.613447150 0.103826154
## 163 164 165 166 167 168
## -0.584795668 -0.797745125 -0.923444321 -0.080705315 -0.362428882 -0.193055134
## 169 170 171 172 173 174
## -0.022549817 -0.528540196 0.017414671 -0.263990755 -0.635740946 -1.006383371
## 175 176 177 178 179 180
## -0.719630746 0.041794680 -0.919307011 -1.240639400 0.153899524 -0.275186941
## 181 182 183 184 185 186
## 0.255706766 -0.622651534 -1.010647658 -1.643449840 -0.706496720 -0.554271322
## 187 188 189 190 191 192
## 0.085125471 -0.153401590 0.196242232 0.466242979 0.101916302 0.132891233
## 193 194 195 196 197 198
## -0.058730517 0.226849953 0.092034675 0.046388800 0.320837843 0.197634154
## 199 200 201 202 203 204
## 0.041543478 -0.084591895 -0.031534623 0.376878462 0.083499436 0.131331710
## 205 206 207 208 209 210
## 0.125611940 0.160134357 -0.025976111 -0.147004743 0.102707357 -0.132043750
## 211 212 213 214 215 216
## 0.142449049 0.222082014 -0.095722886 -0.086447134 0.193431092 0.047369108
## 217 218 219 220 221 222
## -0.236510673 -0.011232245 0.630867557 0.965698775 0.842951821 0.980329919
## 223 224 225 226 227 228
## 0.405603758 -0.081259496 0.020476796 0.198995617 0.539530739 0.695241902
## 229 230 231 232 233 234
## 0.505353089 0.103543071 0.084199783 -0.060773234 -0.687262335 0.223897168
## 235 236 237 238 239 240
## 0.158265282 -0.097488959 -0.063130119 -0.320686525 -0.111602996 0.223043923
## 241 242 243 244 245 246
## 0.069286926 -0.075827417 -0.195341651 0.007382603 -0.155997697 -0.340909232
## 247 248 249 250 251 252
## -0.313957509 -0.278744127 -0.331574026 -0.279316587 -0.669261650 -0.511348060
## 253 254 255 256 257 258
## -0.543592370 -0.567951602 -0.649225670 -0.795434355 -1.068118107 -0.536898969
## 259 260 261 262 263 264
## -0.781653867 -1.378215169 -0.642796987 -0.695479334 -1.133816241 -0.705216939
## 265 266 267 268 269 270
## -0.833183745 -0.481082101 -0.949364510 -0.666934935 -0.729533596 -0.670244008
## 271 272 273 274 275 276
## -0.459775767 -0.312795933 -0.683795518 -0.958265199 -0.710554591 -0.461965690
## 277 278 279 280 281 282
## -1.927703353 -1.860354405 -1.788623255 -0.580177525 -1.364166882 -1.264233742
## 283 284 285 286 287 288
## -1.405559426 -0.994684914 -1.846049333 -1.169577240 -1.522802689 -1.370957154
## 289 290 291 292 293 294
## -1.488322029 -0.898873445 -1.182528558 -1.869183395 -1.303331789 -0.838020471
## 295 296 297 298 299 300
## -0.783640584 -0.184541374 -0.804762372 -0.845862677 -0.639393492 -0.073034083
## 301 302 303 304 305 306
## 0.505106704 -0.414760325 -0.152886163 0.011629339 0.175510337 0.008692918
## 307 308 309 310 311 312
## -0.466941362 -0.303730275 0.212979426 -0.354538102 -0.630846915 -0.610448748
## 313 314 315 316 317 318
## -1.751952004 -1.272773337 -0.374306882 0.290963727 0.046446696 -0.214981661
## 319 320 321 322 323 324
## -0.545341288 -0.332527264 -0.469964243 -0.455682589 -0.018678859 -0.219464918
## 325 326 327 328 329 330
## -0.255516321 0.299562431 0.462774125 -0.712331746 0.204310949 0.378700005
## 331 332 333 334 335 336
## 0.236595198 0.131521713 0.023084524 0.309143039 0.393019139 0.514684828
## 337 338 339 340 341 342
## 0.709765643 0.815688120 0.422194522 0.927938263 1.026089235 0.119582660
## 343 344 345 346 347 348
## -0.400948873 0.618876707 1.283429018 1.428341833 1.416771338 1.546686323
## 349 350 351 352 353 354
## 0.844014152 0.520292465 0.964667125 1.468735348 1.440001829 1.088767430
## 355 356 357 358 359 360
## 1.381710323 1.285408988 0.927875505 0.875859442 1.146208669 1.053124920
## 361 362 363 364 365 366
## 0.992434881 1.103931611 1.235399280 0.792817833 0.536064069 1.022193226
## 367 368 369 370 371 372
## 1.369988900 1.386744406 1.145528674 0.111164949 -0.122587151 0.403142012
## 373 374 375 376 377 378
## 0.917741437 0.574358546 0.414126633 0.390922055 0.409998132 -0.047921889
## 379 380 381 382 383 384
## 0.051743407 0.346350681 0.219834318 0.183649959 0.003918620 -0.087689089
## 385 386 387 388 389 390
## -0.443879508 -0.368255592 -0.233817769 -0.134835441 -0.394255333 -0.319883083
## 391 392 393 394 395 396
## -0.218698343 -0.910699733 -0.465972929 -0.585333047 -0.694596814 -0.586108231
## 397 398 399 400 401 402
## -0.738585332 -0.679538577 -1.118610524 -0.420766359 -0.638185474 -0.714555809
## 403 404 405 406 407 408
## -0.585440652 -0.563505308 -0.878102761 -1.280603695 -1.191681077 -0.934102963
## 409 410 411 412 413 414
## -1.596363594 -1.557809531 -0.722601433 -1.255975639 -0.770097847 -0.727531531
## 415 416 417 418 419 420
## -0.518165467 -1.293445438 -0.778215674 -0.565879295 -0.856861437 -0.400860881
## 421 422 423 424 425 426
## -0.440988575 -0.959018978 -0.689239873 -0.689466316 -0.532029981 -0.278728684
## 427 428 429 430 431 432
## 0.266328315 0.783612944 -0.362063857 -0.402825267 -0.403869896 -0.366283882
## 433 434 435 436 437 438
## -0.063202851 0.165020700 0.151977809 -0.472627095 -0.542580764 -0.820343633
## 439 440 441 442 443 444
## -0.583075855 -0.521115134 -0.403670372 -0.526089683 -0.566016826 -1.104702309
## 445 446 447 448 449 450
## -0.806441249 -0.082094347 -0.979519688 -0.878787309 -0.900340594 -0.696046618
## 451 452 453 454 455 456
## -0.459637216 0.026626468 -0.546385035 -0.882709570 -1.394742797 -1.432171235
## 457 458 459 460 461 462
## -0.853846173 -0.715528872 -1.211671395 -1.384127172 -1.836427085 -0.407158641
## 463 464 465 466 467 468
## -1.607260055 -0.880169779 -0.844179745 -0.666642593 -0.660131954 -0.278294858
## 469 470 471 472 473 474
## -1.266666170 -1.041434986 -0.633569678 -0.426953761 -0.315162411 -0.559516785
## 475 476
## -0.196315618 -0.496435946
png(filename = "DL_res.png", units = "cm", res = 700,
width = 20, height = 15)
grid.arrange(wake_mod_dl14_res,
meck_mod_dl14_res,
hanover_mod_dl14_res)
dev.off()
## quartz_off_screen
## 2
#DL forecasting plots#
full_cases_wastewater_weather_data_test <-
cbind(full_cases_wastewater_weather_data_test,f_dl14$forecasts[,2],
f_dl14$forecasts[,1],f_dl14$forecasts[,3])
full_cases_wastewater_weather_data_meck_test <-
cbind(full_cases_wastewater_weather_data_meck_test,f_dl14_meck$forecasts[,2],
f_dl14_meck$forecasts[,1],f_dl14_meck$forecasts[,3])
full_cases_wastewater_weather_data_hanover_test <-
cbind(full_cases_wastewater_weather_data_hanover_test,f_dl14_hanover$forecasts[,2],
f_dl14_hanover$forecasts[,1],f_dl14_hanover$forecasts[,3])
wake_dl_plot <- full_cases_wastewater_weather_data_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_test, aes(ymin = f_dl14$forecasts[,1], ymax = f_dl14$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_test,aes(Date,f_dl14$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
meck_dl_plot <- full_cases_wastewater_weather_data_meck_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_meck_test, aes(ymin = f_dl14_meck$forecasts[,1], ymax = f_dl14_meck$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_meck_test,aes(Date,f_dl14_meck$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
hanover_dl_plot <- full_cases_wastewater_weather_data_hanover_train %>%
ggplot(aes(Date,log_mean_new_cases)) +
geom_line() +
geom_ribbon(data = full_cases_wastewater_weather_data_hanover_test, aes(ymin = f_dl14_hanover$forecasts[,1], ymax = f_dl14_hanover$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,log_mean_new_cases,color="Actual")) +
geom_line(data = full_cases_wastewater_weather_data_hanover_test,aes(Date,f_dl14_hanover$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "bottom") + ylab("")
png(filename = "dl_plots.png",res = 700, units = "cm",
width = 20,height = 15)
grid.arrange(wake_dl_plot,
meck_dl_plot,
hanover_dl_plot,
ncol=1,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2
Sensitivity analysis
#Cases
cases <- read.csv("cases_by_county.csv")
glimpse(cases)
## Rows: 158,340
## Columns: 6
## $ X <int> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …
## $ date <chr> "2021-11-20", "2021-11-23", "2…
## $ rolling_average_cases_per_100k_centered <dbl> 58.628121, 53.867485, 46.16043…
## $ state <chr> "AZ", "AZ", "AZ", "AZ", "AZ", …
## $ name <chr> "Pima County, AZ", "Pima Count…
## $ fipscode <int> 4019, 4019, 4019, 4019, 4019, …
cases <- cases[order(as.Date(cases$date)),]
cases <- cases[cases$date >= "2021-01-04" &
cases$date <= "2022-05-22",]
cases_nc <- cases %>% dplyr::filter(state == "NC")
glimpse(cases_nc)
## Rows: 1,512
## Columns: 6
## $ X <int> 56308, 103759, 116281, 16478, …
## $ date <chr> "2021-01-04", "2021-01-04", "2…
## $ rolling_average_cases_per_100k_centered <dbl> 63.71797, 101.44618, 55.99169,…
## $ state <chr> "NC", "NC", "NC", "NC", "NC", …
## $ name <chr> "Duplin County, NC", "Stanly C…
## $ fipscode <int> 37061, 37167, 37051, 37167, 37…
cases_nc <- cases_nc %>% group_by(date) %>% summarise(mean_cases=
mean(rolling_average_cases_per_100k_centered))
#Wastewater
wastewater <- read.csv("wastewater_by_county.csv")
glimpse(wastewater)
## Rows: 6,562
## Columns: 7
## $ X <int> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …
## $ sampling_week <chr> "2020-01-01", "2020-01-15", "2…
## $ effective_concentration_rolling_average <dbl> 134.841964, 0.000000, 0.000000…
## $ region <chr> "Midwest", "Northeast", "North…
## $ state <chr> "IL", "MA", "MA", "MA", "MA", …
## $ name <chr> "Peoria County, IL", "Suffolk …
## $ fipscode <int> 17143, 25025, 25025, 25025, 25…
wastewater <- wastewater[order(as.Date(wastewater$sampling_week)),]
wastewater <- wastewater[wastewater$sampling_week >= "2021-01-04" &
wastewater$sampling_week <= "2022-05-22",]
wastewater_nc <- wastewater %>% dplyr::filter(state == "NC")
glimpse(wastewater_nc)
## Rows: 38
## Columns: 7
## $ X <int> 1662, 1735, 1739, 1825, 1830, …
## $ sampling_week <chr> "2021-06-09", "2021-06-16", "2…
## $ effective_concentration_rolling_average <dbl> 162.00024, 305.01615, 81.08650…
## $ region <chr> "South", "South", "South", "So…
## $ state <chr> "NC", "NC", "NC", "NC", "NC", …
## $ name <chr> "Cumberland County, NC", "Cumb…
## $ fipscode <int> 37051, 37051, 37061, 37051, 37…
wastewater_nc <- wastewater_nc %>% group_by(sampling_week) %>%
summarise(mean_wastewater = mean(effective_concentration_rolling_average))
wastewater_nc$sampling_week <- as.Date(wastewater_nc$sampling_week)
wastewater_nc <- pad(wastewater_nc,start_val=as.Date("2021-01-04"),
end_val=as.Date("2022-05-22"))
wastewater_nc <- wastewater_nc %>%
mutate(mean_wastewater = na_locf(mean_wastewater,))
colnames(wastewater_nc)[1] <-"date"
#merge dataset
nc_data <- cbind(cases_nc,wastewater_nc[,-1])
glimpse(nc_data)
## Rows: 504
## Columns: 3
## $ date <chr> "2021-01-04", "2021-01-05", "2021-01-06", "2021-01-07"…
## $ mean_cases <dbl> 73.71861, 89.17613, 79.05748, 83.65169, 82.17460, 83.8…
## $ mean_wastewater <dbl> 162.0002, 162.0002, 162.0002, 162.0002, 162.0002, 162.…
nc_data$date <- as.Date(nc_data$date)
#Line plots
png(filename = "line_plot_sensitivity_analysis.png",units = "cm",res = 700,
width = 20, height = 14)
case_plot <- nc_data %>% ggplot(aes(date,mean_cases)) + geom_line() +
ylab("COVID-19 case counts per 100k") + theme_bw()
ww_plot <- nc_data %>% ggplot(aes(date,mean_wastewater)) + geom_line() +
ylab("Viral gene copies per mL") + theme_bw()
grid.arrange(case_plot,
ww_plot)
dev.off()
## quartz_off_screen
## 2
#Correlations
png(filename = "nc_cor.png",units = "cm",res = 700,
width = 20, height = 8)
nc_data %>% ggplot(aes(mean_wastewater,mean_cases)) + geom_point() +
theme_bw() + xlab("Viral gene copies per mL") + ylab("New Cases")
dev.off()
## quartz_off_screen
## 2
cor.test(nc_data$mean_cases,nc_data$mean_wastewater)
##
## Pearson's product-moment correlation
##
## data: nc_data$mean_cases and nc_data$mean_wastewater
## t = 14.884, df = 502, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4896649 0.6111462
## sample estimates:
## cor
## 0.5533411
#arima
cases <- xts(nc_data$mean_cases, order.by = nc_data$date)
attr(cases, 'frequency') <- 7
periodicity(cases)
## Daily periodicity from 2021-01-04 to 2022-05-22
cases <- as.ts(cases)
#plot(decompose(log(cases)))
cases_deseasonalise <- seasadj(decompose(log(cases)))
cases_deseasonalise_train <- cases_deseasonalise[-c(491:504)]
cases_deseasonalise_test <- cases_deseasonalise[c(491:504)]
lowest_rmse<-Inf
lowest_mae<-Inf
best_mod<-NULL
best_mod_mae<-NULL
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(cases_deseasonalise_train, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
rmse_mod_1 <- rmse(cases_deseasonalise_test,forecast_fit$mean)
if (rmse_mod_1 < lowest_rmse){
lowest_rmse <- rmse_mod_1
best_mod <- arima_mod_1
}
}
}
lowest_rmse
## [1] 0.3455963
best_mod #arima(3,1,1)
## Series: cases_deseasonalise_train
## ARIMA(3,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.6336 0.1419 0.1348 -0.8879
## s.e. 0.0746 0.0541 0.0456 0.0620
##
## sigma^2 = 0.03666: log likelihood = 116.4
## AIC=-222.8 AICc=-222.67 BIC=-201.84
for (p in seq(1:4)){
for (q in seq(1:4)){
arima_mod_1 <- Arima(cases_deseasonalise_train, order = c(p,1,q))
forecast_fit <- forecast::forecast(arima_mod_1,h=14)
mae_mod <- mae(cases_deseasonalise_test,forecast_fit$mean)
if (mae_mod < lowest_mae){
lowest_mae <- mae_mod
best_mod_mae <- arima_mod_1
}
}
}
best_mod_mae
## Series: cases_deseasonalise_train
## ARIMA(3,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.6336 0.1419 0.1348 -0.8879
## s.e. 0.0746 0.0541 0.0456 0.0620
##
## sigma^2 = 0.03666: log likelihood = 116.4
## AIC=-222.8 AICc=-222.67 BIC=-201.84
lowest_mae #arima(3,1,1)
## [1] 0.2671189
best_arima_mod <- Arima(cases_deseasonalise_train, order = c(3,1,1))
best_arima_mod_forecast <- forecast::forecast(best_arima_mod,h=14)
rmse(cases_deseasonalise_test,best_arima_mod_forecast$mean)
## [1] 0.3455963
mae(cases_deseasonalise_test,best_arima_mod_forecast$mean)
## [1] 0.2671189
checkresiduals(best_arima_mod)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,1)
## Q* = 32.905, df = 6, p-value = 1.093e-05
##
## Model df: 4. Total lags used: 10
png(filename = "sensitivity_nc_arima.png",res = 700, units = "cm",
width = 20, height = 10)
arima_plot <- autoplot(best_arima_mod_forecast) +
autolayer(best_arima_mod_forecast, series = "Forecasted") +
autolayer(ts(cases_deseasonalise_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time")+
ggtitle(NULL) + theme(legend.position = "none")
dev.off()
## quartz_off_screen
## 2
exp(cases_deseasonalise_test[1])
## [1] 11.68326
exp(best_arima_mod_forecast$mean[1])
## [1] 12.25043
exp(best_arima_mod_forecast$lower[1,])
## 80% 95%
## 9.584871 8.417325
exp(best_arima_mod_forecast$upper[1,])
## 80% 95%
## 15.65728 17.82906
exp(best_arima_mod_forecast$mean[1])-exp(cases_deseasonalise_test[1])
## [1] 0.5671695
exp(cases_deseasonalise_test[7])
## [1] 18.14823
exp(best_arima_mod_forecast$mean[7])
## [1] 12.36624
exp(best_arima_mod_forecast$lower[7,])
## 80% 95%
## 7.170108 5.373013
exp(best_arima_mod_forecast$upper[7,])
## 80% 95%
## 21.32798 28.46147
exp(best_arima_mod_forecast$mean[7])-exp(cases_deseasonalise_test[7])
## [1] -5.781993
exp(cases_deseasonalise_test[14])
## [1] 25.32937
exp(best_arima_mod_forecast$mean[14])
## [1] 12.45729
exp(best_arima_mod_forecast$lower[14,])
## 80% 95%
## 5.440607 3.509080
exp(best_arima_mod_forecast$upper[14,])
## 80% 95%
## 28.52332 44.22360
exp(best_arima_mod_forecast$mean[14])-exp(cases_deseasonalise_test[14])
## [1] -12.87208
#SARIMA
cases_train <- log(cases)[-c(491:504)]
cases_test <- log(cases)[c(491:504)]
sarima_rmse <- Inf
sarima_best_mod <-NULL
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(cases_train, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
rsme_mod <- rmse(cases_test,forecast_fit$mean)
if(rsme_mod<sarima_rmse){
sarima_rmse<- rsme_mod
sarima_best_mod<-sarima_mod_1
}
}
}
}
}
}
}
sarima_rmse
## [1] 0.04706877
sarima_best_mod #arima(0,3,3)(1,3,2)[7]
## Series: cases_train
## ARIMA(0,3,3)(1,3,2)[7]
##
## Coefficients:
## ma1 ma2 ma3 sar1 sma1 sma2
## -2.2331 1.5617 -0.3285 -0.7234 -1.7973 0.8678
## s.e. NaN NaN NaN NaN 0.0180 NaN
##
## sigma^2 = 0.08438: log likelihood = -85.66
sarima_mae <- Inf
sarima_best_mod_mae <-NULL
for (p in seq(0,3)){
for (d in seq(0,3)){
for (q in seq(0,3)){
for (P in seq(0,3)){
for (D in seq(0,3)){
for (Q in seq(0,3)){
sarima_mod_1 <- Arima(cases_train, order = c(p,d,q),
seasonal = list(order=c(P,D,Q),period=7),
method="CSS")
forecast_fit <- forecast::forecast(sarima_mod_1,14)
mae_mod <- mae(cases_test,forecast_fit$mean)
if(mae_mod<sarima_mae){
sarima_mae<- mae_mod
sarima_best_mod_mae<-sarima_mod_1
}
}
}
}
}
}
}
sarima_mae
## [1] 0.03468064
sarima_best_mod_mae
## Series: cases_train
## ARIMA(0,3,2)(3,2,2)[7]
##
## Coefficients:
## ma1 ma2 sar1 sar2 sar3 sma1 sma2
## -1.9398 0.9407 -0.6269 -0.3011 -0.0470 -1.3960 0.4249
## s.e. 0.0023 0.0024 0.1282 0.1152 0.0174 0.1607 0.1631
##
## sigma^2 = 0.05142: log likelihood = 23.5
sarima_best_mod_1 <- Arima(cases_train, order = c(0,3,3),
seasonal = list(order=c(1,3,2),period=7),
method="CSS")
sarima_best_mod_1_forecast <- forecast::forecast(sarima_best_mod_1,14)
rmse(cases_test,sarima_best_mod_1_forecast$mean)
## [1] 0.04706877
mae(cases_test,sarima_best_mod_1_forecast$mean)
## [1] 0.03691424
checkresiduals(sarima_best_mod_1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,3,3)(1,3,2)[7]
## Q* = 8.9851, df = 4, p-value = 0.06147
##
## Model df: 6. Total lags used: 10
sarima_best_mod_3 <- Arima(cases_train, order = c(0,3,2),
seasonal = list(order=c(3,2,2),period=7),
method="CSS")
coeftest(sarima_best_mod_3)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -1.9398426 0.0022785 -851.3765 < 2.2e-16 ***
## ma2 0.9407284 0.0024320 386.8186 < 2.2e-16 ***
## sar1 -0.6268993 0.1281771 -4.8909 1.004e-06 ***
## sar2 -0.3010714 0.1152230 -2.6129 0.008977 **
## sar3 -0.0469942 0.0173562 -2.7076 0.006776 **
## sma1 -1.3959982 0.1606967 -8.6872 < 2.2e-16 ***
## sma2 0.4249349 0.1630928 2.6055 0.009175 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sarima_best_mod_3_forecast <- forecast::forecast(sarima_best_mod_3,14)
rmse(cases_test,sarima_best_mod_3_forecast$mean)
## [1] 0.04984621
mae(cases_test,sarima_best_mod_3_forecast$mean)
## [1] 0.03468064
checkresiduals(sarima_best_mod_3)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,3,2)(3,2,2)[7]
## Q* = 32.82, df = 3, p-value = 3.514e-07
##
## Model df: 7. Total lags used: 10
png(filename = "sensitivity_nc_sarima_simple.png",res = 700, units = "cm",
width = 20, height = 10)
sarima_plot <- autoplot(sarima_best_mod_3_forecast) +
autolayer(sarima_best_mod_3_forecast, series = "Forecasted") +
autolayer(ts(cases_deseasonalise_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time")+
ggtitle(NULL) + theme(legend.position = "none")
dev.off()
## quartz_off_screen
## 2
exp(cases_deseasonalise_test[1])
## [1] 11.68326
exp(sarima_best_mod_3_forecast$mean[1])
## [1] 11.80592
exp(sarima_best_mod_3_forecast$lower[1,])
## 80% 95%
## 8.831264 7.573240
exp(sarima_best_mod_3_forecast$upper[1,])
## 80% 95%
## 15.78254 18.40425
exp(sarima_best_mod_3_forecast$mean[1])-exp(cases_test[1])
## [1] -0.08975849
exp(cases_deseasonalise_test[7])
## [1] 18.14823
exp(sarima_best_mod_3_forecast$mean[7])
## [1] 17.80267
exp(sarima_best_mod_3_forecast$lower[7,])
## 80% 95%
## 7.127076 4.389838
exp(sarima_best_mod_3_forecast$upper[7,])
## 80% 95%
## 44.46918 72.19747
exp(sarima_best_mod_3_forecast$mean[7])-exp(cases_test[7])
## [1] -0.8412984
exp(cases_deseasonalise_test[14])
## [1] 25.32937
exp(sarima_best_mod_3_forecast$mean[14])
## [1] 23.16659
exp(sarima_best_mod_3_forecast$lower[14,])
## 80% 95%
## 4.934803 2.176459
exp(sarima_best_mod_3_forecast$upper[14,])
## 80% 95%
## 108.7563 246.5891
exp(sarima_best_mod_3_forecast$mean[14])-exp(cases_test[14])
## [1] -2.854685
#multivariate modelling#
#ARIMAX, with water
viral_deseasonalise <- seasadj(decompose(ts(log(nc_data$mean_wastewater),
frequency = 7)))
viral_deseasonalise_train <- viral_deseasonalise[-c(491:504)]
viral_deseasonalise_test <- viral_deseasonalise[c(491:504)]
wastewater_mod <- Arima(cases_deseasonalise_train ,order = c(3,1,1),
xreg = viral_deseasonalise_train)
coeftest(wastewater_mod)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.632174 0.072198 8.7561 < 2.2e-16 ***
## ar2 0.142602 0.053842 2.6485 0.008085 **
## ar3 0.137426 0.045916 2.9930 0.002763 **
## ma1 -0.886679 0.059077 -15.0089 < 2.2e-16 ***
## xreg -0.048612 0.082454 -0.5896 0.555482
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast_mod_1 <- forecast::forecast(wastewater_mod, h=14,
xreg = viral_deseasonalise_test)
rmse(cases_deseasonalise_test,forecast_mod_1$mean)
## [1] 0.3456571
mae(cases_deseasonalise_test,forecast_mod_1$mean)
## [1] 0.2662839
tsdisplay(residuals(wastewater_mod))
png(filename = "sensitivity_nc_arimax.png",res = 700, units = "cm",
width = 20, height = 10)
arimax_plot <- autoplot(forecast_mod_1) +
autolayer(forecast_mod_1 , series = "Forecasted") +
autolayer(ts(cases_deseasonalise_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time") +
ggtitle(NULL) + theme(legend.position = "none")
dev.off()
## quartz_off_screen
## 2
exp(cases_deseasonalise_test[1])
## [1] 11.68326
exp(forecast_mod_1$mean[1])
## [1] 12.2664
exp(forecast_mod_1$lower[1,])
## 80% 95%
## 9.595798 8.426193
exp(forecast_mod_1$upper[1,])
## 80% 95%
## 15.68025 17.85677
exp(forecast_mod_1$mean[1])-exp(cases_deseasonalise_test[1])
## [1] 0.5831395
exp(cases_deseasonalise_test[7])
## [1] 18.14823
exp(forecast_mod_1$mean[7])
## [1] 12.32183
exp(forecast_mod_1$lower[7,])
## 80% 95%
## 7.126134 5.332845
exp(forecast_mod_1$upper[7,])
## 80% 95%
## 21.30574 28.47027
exp(forecast_mod_1$mean[7])-exp(cases_deseasonalise_test[7])
## [1] -5.8264
exp(cases_deseasonalise_test[14])
## [1] 25.32937
exp(forecast_mod_1$mean[14])
## [1] 12.47918
exp(forecast_mod_1$lower[14,])
## 80% 95%
## 5.404005 3.469813
exp(forecast_mod_1$upper[14,])
## 80% 95%
## 28.81751 44.88136
exp(forecast_mod_1$mean[14])-exp(cases_deseasonalise_test[14])
## [1] -12.85019
#SARIMAX, with water
viral_train <- log(nc_data$mean_wastewater)[-c(491:504)]
viral_test <- log(nc_data$mean_wastewater)[c(491:504)]
sarimax_wastewater_mod <- Arima(cases_train ,order = c(0,3,2),
seasonal = list(order=c(3,2,2),period=7),
xreg = viral_train,
method = "CSS-ML")
coeftest(sarimax_wastewater_mod)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -1.9601395 0.0032763 -598.2782 <2e-16 ***
## ma2 0.9604238 0.0032989 291.1352 <2e-16 ***
## sar1 -0.5922529 0.0014546 -407.1487 <2e-16 ***
## sar2 -0.2887453 0.0035108 -82.2441 <2e-16 ***
## sar3 -0.0703806 0.0042554 -16.5391 <2e-16 ***
## sma1 -1.4521516 0.0031877 -455.5529 <2e-16 ***
## sma2 0.4574305 0.0096941 47.1866 <2e-16 ***
## xreg -0.0323508 0.0799103 -0.4048 0.6856
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sarimax_wastewater_mod_forecast <- forecast::forecast(sarimax_wastewater_mod, h=14,
xreg = viral_test)
rmse(cases_test,sarimax_wastewater_mod_forecast$mean)
## [1] 0.06608591
mae(cases_test,sarimax_wastewater_mod_forecast$mean)
## [1] 0.05076526
checkresiduals(sarimax_wastewater_mod)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(0,3,2)(3,2,2)[7] errors
## Q* = 36.206, df = 3, p-value = 6.773e-08
##
## Model df: 8. Total lags used: 11
png(filename = "sensitivity_nc_sarimax_complex.png",res = 700, units = "cm",
width = 20, height = 10)
sarimax_plot <- autoplot(sarimax_wastewater_mod_forecast) +
autolayer(sarimax_wastewater_mod_forecast, series = "Forecasted") +
autolayer(ts(cases_test,start = 491), series = "Observed") +
theme_bw(base_size = 15) + ylab("") + xlab("Time") +
ggtitle(NULL) + theme(legend.position = "none")
dev.off()
## quartz_off_screen
## 2
exp(sarimax_wastewater_mod_forecast$mean[1])
## [1] 11.76755
exp(sarimax_wastewater_mod_forecast$lower[1,])
## 80% 95%
## 8.913452 7.694546
exp(sarimax_wastewater_mod_forecast$upper[1,])
## 80% 95%
## 15.53552 17.99653
exp(sarimax_wastewater_mod_forecast$mean[1])-exp(cases_test[1])
## [1] -0.1281357
exp(sarimax_wastewater_mod_forecast$mean[7])
## [1] 17.19558
exp(sarimax_wastewater_mod_forecast$lower[7,])
## 80% 95%
## 7.484325 4.818489
exp(sarimax_wastewater_mod_forecast$upper[7,])
## 80% 95%
## 39.50765 61.36531
exp(sarimax_wastewater_mod_forecast$mean[7])-exp(cases_test[7])
## [1] -1.448389
exp(sarimax_wastewater_mod_forecast$mean[14])
## [1] 22.66054
exp(sarimax_wastewater_mod_forecast$lower[14,])
## 80% 95%
## 6.037109 2.997355
exp(sarimax_wastewater_mod_forecast$upper[14,])
## 80% 95%
## 85.05725 171.31765
exp(sarimax_wastewater_mod_forecast$mean[14])-exp(cases_test[14])
## [1] -3.360739
#Autoregressive Distributed Lag Model
nc_data <- nc_data %>%
mutate(log_cases = log(mean_cases),
log_viral = log(mean_wastewater))
nc_data <- nc_data %>%
mutate(log_cases = seasadj(decompose(ts(log_cases,frequency = 7))),
log_viral = seasadj(decompose(ts(log_viral,frequency = 7))))
nc_data_train <- nc_data[-c(491:504),]
nc_data_test <- nc_data[c(491:504),]
lowest_rmse_ardl <- Inf
best_mod_ardl <- NULL
for (p in seq(1,14)){
for (q in seq(1,14)){
mod <- ardlDlm(log_cases ~ log_viral,
data = nc_data_train, p=p,q=q)
f <- forecast(mod, x= t(nc_data_test[,5]),h=14)
forecast_acc <- rmse(nc_data_test[,4],
f$forecasts)
if (forecast_acc<lowest_rmse_ardl){
lowest_rmse_ardl<- forecast_acc
best_mod_ardl <- mod
}
}
}
lowest_rmse_ardl #0.153
## [1] 0.1527168
summary(best_mod_ardl) #ardl(1,14), similar to wake
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90992 -0.04728 -0.00450 0.03391 1.82292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0510420 0.0547900 -0.932 0.35204
## log_viral.t 0.0068198 0.0962389 0.071 0.94354
## log_viral.1 -0.0004429 0.1355423 -0.003 0.99739
## log_viral.2 -0.0662456 0.1355423 -0.489 0.62526
## log_viral.3 -0.0267071 0.1355444 -0.197 0.84389
## log_viral.4 0.3559041 0.1355462 2.626 0.00894 **
## log_viral.5 -0.2269657 0.1359995 -1.669 0.09582 .
## log_viral.6 -0.0071780 0.1363630 -0.053 0.95804
## log_viral.7 -0.0289224 0.1364897 -0.212 0.83228
## log_viral.8 -0.0003262 0.1361771 -0.002 0.99809
## log_viral.9 0.1139565 0.1361771 0.837 0.40313
## log_viral.10 -0.0872283 0.1361834 -0.641 0.52215
## log_viral.11 0.0869370 0.1361774 0.638 0.52353
## log_viral.12 -0.0677954 0.1362716 -0.498 0.61907
## log_viral.13 0.0133665 0.1363593 0.098 0.92196
## log_viral.14 -0.0393125 0.0967766 -0.406 0.68477
## log_cases.1 0.9662545 0.0113959 84.790 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1981 on 459 degrees of freedom
## Multiple R-squared: 0.9661, Adjusted R-squared: 0.9649
## F-statistic: 818.1 on 16 and 459 DF, p-value: < 2.2e-16
checkresiduals(best_mod_ardl)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## -0.0079361204 0.0749551140 0.0104102776 0.0417587039 0.1788979741
## 20 21 22 23 24
## -0.0197832873 -0.0636556796 0.0659424356 -0.0058961325 0.0563267039
## 25 26 27 28 29
## 0.0722532860 0.0555601394 0.0195105611 0.1191322887 0.0569816684
## 30 31 32 33 34
## 0.0432000544 0.0106782259 0.0277613061 0.0608521145 0.0164457056
## 35 36 37 38 39
## -0.1385073028 0.0055273619 0.0465037029 0.0195600474 -0.0073049436
## 40 41 42 43 44
## 0.0448363228 0.0049317851 -0.0320415286 0.0338699326 0.0305961503
## 45 46 47 48 49
## 0.0283465099 0.0926974719 0.0618128861 -0.0184534334 0.0213206569
## 50 51 52 53 54
## 0.0326426656 -0.0040375544 -0.0371331073 -0.1782426977 0.2204057225
## 55 56 57 58 59
## 0.0104794007 -0.0693380908 -0.0828500659 0.0462878989 0.0246169661
## 60 61 62 63 64
## 0.0262632746 -0.0843961025 -0.0379274320 -0.0720000488 0.0817978511
## 65 66 67 68 69
## -0.0246907811 -0.1745607217 0.0117215188 0.2851422174 0.0443775771
## 70 71 72 73 74
## 0.0028641604 -0.0653787188 0.0414945238 0.1727227919 0.0492103829
## 75 76 77 78 79
## -0.1762951948 -0.0672963539 -0.0814167277 0.1228827473 0.0513663051
## 80 81 82 83 84
## -0.1715105563 -0.0272278816 0.3267267423 0.0269302279 -0.0049594610
## 85 86 87 88 89
## -0.0068720516 -0.1771227030 0.0139272167 0.0124382865 0.0116317455
## 90 91 92 93 94
## -0.0586408875 -0.0057825049 -0.0022346363 0.2057315708 0.0174397517
## 95 96 97 98 99
## 0.0159508215 0.0837310328 0.0630946687 -0.0019086285 0.0872437669
## 100 101 102 103 104
## 0.0692130295 0.0246579464 0.0231690162 0.0438558048 -0.0308327461
## 105 106 107 108 109
## -0.0682791666 0.0288945455 0.0165520992 0.0209345474 0.0194456172
## 110 111 112 113 114
## 0.0187354925 0.0234234992 0.0130892478 0.0212016080 0.0359539623
## 115 116 117 118 119
## 0.0216787007 0.0201897705 -0.0124944339 0.0329172523 -0.0371419702
## 120 121 122 123 124
## -0.0537262902 0.0013843828 0.0164835277 0.0149945975 0.0220603837
## 125 126 127 128 129
## -0.1017259910 0.0188264098 -0.0081172809 -0.0540654425 0.0104045561
## 130 131 132 133 134
## 0.0089156258 -0.0880293066 0.0128322586 -0.1653236580 0.0155740275
## 135 136 137 138 139
## -0.0111191180 0.0019533161 0.0004643858 -0.1051715333 -0.0873028623
## 140 141 142 143 144
## -0.1879690028 -0.0661025606 -0.0561235139 -0.0136130746 -0.0151020048
## 145 146 147 148 149
## -0.6491330093 0.5089412804 0.0198081074 -0.2184427088 -0.0626808175
## 150 151 152 153 154
## -0.0232161815 -0.0247051117 0.3079386518 -0.6193300126 -0.0351904552
## 155 156 157 158 159
## -0.0414229027 0.0188372528 -0.0307096957 -0.0321986260 -0.0149869349
## 160 161 162 163 164
## -0.0036051011 -0.0757256960 -0.0116401080 -0.1742037359 -0.0357920263
## 165 166 167 168 169
## -0.0372032920 -0.2483563235 -0.2813997227 -0.1067490983 -0.0787267436
## 170 171 172 173 174
## 0.0786696808 -0.0471878676 -0.0486563388 0.2077356296 0.0019712878
## 175 176 177 178 179
## -0.0805729466 0.0865198432 0.0129930756 -0.0336060184 -0.0351717909
## 180 181 182 183 184
## -0.5430052770 0.5699702406 -0.0347356633 -0.0104205063 -0.0060264274
## 185 186 187 188 189
## -0.0281139827 -0.0296381870 0.7002595730 -0.1527768573 0.1775209363
## 190 191 192 193 194
## 0.1674719834 0.1528291914 0.0072232150 0.0059096600 0.2073372355
## 195 196 197 198 199
## 0.0335530920 -0.1284625207 0.0521549363 0.1490383312 0.0134896319
## 200 201 202 203 204
## 0.0124702152 0.2319947813 0.1609154434 -0.1409760511 0.1574839305
## 205 206 207 208 209
## 0.0712239389 0.0229084624 0.0220056565 0.1333588061 0.2773868323
## 210 211 212 213 214
## -0.4082967438 -0.0289206932 -0.0188004247 0.0180399290 0.0166556427
## 215 216 217 218 219
## 0.1653146892 -0.2047006295 0.1675126483 0.0762783587 0.0738031871
## 220 221 222 223 224
## 0.0143720963 0.0128985843 0.0468493669 0.0396119258 -0.0621725083
## 225 226 227 228 229
## 0.0147808954 0.0266446386 0.0170979071 0.0158166921 0.1304838681
## 230 231 232 233 234
## 0.0297638686 -0.1115102331 0.0400706930 0.0234368102 0.0175708037
## 235 236 237 238 239
## 0.0161697623 0.0459638561 -0.0108645017 -0.0137342257 -0.0215486015
## 240 241 242 243 244
## -0.0174015080 0.0122976291 0.0108086989 -0.5462422658 0.4987813802
## 245 246 247 248 249
## -0.0827648429 -0.0078687278 -0.0051523814 0.0069010163 0.0054120861
## 250 251 252 253 254
## 0.5476827967 -0.3030223961 -0.0066957590 0.0184288810 0.1092836405
## 255 256 257 258 259
## 0.0172406784 0.0157517482 -0.2118031721 -0.0219490663 -0.0494768935
## 260 261 262 263 264
## -0.0182412713 -0.0355656984 0.0047338360 0.0032449058 -0.0303316544
## 265 266 267 268 269
## -0.0461200114 -0.0402549344 0.0040586207 -0.0396813616 -0.0003193617
## 270 271 272 273 274
## -0.0018082919 -0.0109040051 -0.0518081474 -0.0831792400 0.0242242065
## 275 276 277 278 279
## -0.0054861990 -0.0037181888 -0.0052071191 -0.0785204405 -0.0515469270
## 280 281 282 283 284
## -0.0901820582 -0.0732495831 -0.0398027942 -0.0131189694 -0.0146078997
## 285 286 287 288 289
## -0.1030378317 -0.0585937511 -0.0740603660 -0.0188162420 -0.0889480916
## 290 291 292 293 294
## -0.0213484116 -0.0228373419 -0.0009888652 -0.0583160775 -0.0933343153
## 295 296 297 298 299
## -0.2939240825 0.2093383182 -0.0247814122 -0.0262703424 -0.1015690145
## 300 301 302 303 304
## -0.0390658512 -0.1067096847 0.1278524620 -0.2962888130 -0.0337768716
## 305 306 307 308 309
## -0.0352658018 0.0648706161 -0.0386313636 -0.0412756075 -0.2067728246
## 310 311 312 313 314
## 0.2027474944 -0.0284536161 -0.0299425463 -0.1194382612 -0.0796777732
## 315 316 317 318 319
## -0.0893594924 0.1835312754 -0.2090382615 -0.0333254430 -0.0348143732
## 320 321 322 323 324
## 0.0695995113 -0.1067974520 -0.1118620619 -0.2982037909 -0.3142264635
## 325 326 327 328 329
## -0.0526601978 -0.0541491280 0.2644388950 -0.0093278635 0.0558597065
## 330 331 332 333 334
## 0.2707293092 0.1847381877 -0.0195737102 -0.0210626404 0.1126526669
## 335 336 337 338 339
## 0.0332107496 0.0273795097 0.0511426205 0.0341275014 -0.0080152001
## 340 341 342 343 344
## -0.0095041303 -0.0069758511 -0.0526065691 -0.0957398444 -0.0090761737
## 345 346 347 348 349
## 0.0160888997 -0.0108625075 -0.0123514377 -0.0010008676 -0.0228389005
## 350 351 352 353 354
## -0.0472800585 -0.2545202184 -0.2846204474 -0.0288026761 -0.0302916063
## 355 356 357 358 359
## -0.9058903735 1.5652411290 -0.1628820768 0.3315450181 0.0155505485
## 360 361 362 363 364
## 0.0034116287 0.0019226985 0.7549825649 -0.2684037661 0.2725795109
## 365 366 367 368 369
## 0.1214239086 0.2670232421 0.0389337198 0.0374447896 0.1721576193
## 370 371 372 373 374
## 0.0861561917 0.0188683809 0.1833389820 0.1157649150 0.0514240222
## 375 376 377 378 379
## 0.0499350920 -0.3315783638 0.6859096507 0.0254283685 0.0111584290
## 380 381 382 383 384
## -0.0978447114 0.0527690387 0.0512801085 0.6068872423 -0.3934194425
## 385 386 387 388 389
## -0.0123567000 0.1404074447 0.2065508315 0.0566622114 0.0555163791
## 390 391 392 393 394
## -0.2125527694 0.0638413436 -0.2490112019 -0.1070191973 -0.0657752020
## 395 396 397 398 399
## 0.0397380690 0.0381994992 -0.3181207230 -0.1465143113 0.1600813958
## 400 401 402 403 404
## -0.1376118862 -0.0233191256 0.0146532435 0.0125864130 -0.0450035769
## 405 406 407 408 409
## -0.0729973980 0.1954139556 0.0725111900 -0.0485840740 0.0192594298
## 410 411 412 413 414
## 0.0173593428 -0.0300150667 -0.1064081660 -0.0606890359 -0.1471772732
## 415 416 417 418 419
## -0.0472908167 0.0136989670 0.0117901025 -0.3343997815 -0.0541140700
## 420 421 422 423 424
## 0.0739029076 -0.0423713434 -0.0573320347 0.0012472156 -0.0006758919
## 425 426 427 428 429
## 0.0103248355 -0.0569044785 0.1365386768 -0.0364978247 0.0830236429
## 430 431 432 433 434
## 0.0121966072 0.0103500213 -0.0807190521 -0.1064033790 0.0816416569
## 435 436 437 438 439
## -0.0374279359 -0.0177343901 0.0083650951 0.0066315216 0.1274158456
## 440 441 442 443 444
## 0.0340155770 0.1250497496 0.1538768441 0.1140251474 0.0283837841
## 445 446 447 448 449
## 0.0267832477 0.1310663625 -0.0160997119 0.0922018757 0.0438603288
## 450 451 452 453 454
## -0.0559222034 0.0299940801 0.0285615872 -0.0548322644 -0.0089794018
## 455 456 457 458 459
## -0.2664375111 -0.3134873862 -0.3155900116 -0.0083381840 -0.0094403393
## 460 461 462 463 464
## -0.8998684248 -0.9099201774 1.8229177938 -0.0278178361 -0.0187554169
## 465 466 467 468 469
## -0.0060663639 -0.0070574181 -0.0236574378 0.0089609705 -0.1985607999
## 470 471 472 473 474
## -0.0516989335 -0.0506748450 -0.0188521589 -0.0200424954 -0.0440537621
## 475 476 477 478 479
## -0.0327497766 0.4277819064 -0.0278734106 -0.0275121563 -0.0096476569
## 480 481 482 483 484
## -0.0110513494 -0.0102416409 -0.0353550298 -0.0551953313 -0.0147304285
## 485 486 487 488 489
## -0.0113245502 -0.0152254509 -0.0166016525 0.0249369224 -0.0137193043
## 490
## -0.2448440774
mod_ardl114 <- ardlDlm(log_cases ~ log_viral,
data = nc_data_train,p=14,q=1)
summary(mod_ardl114)
##
## Time series regression with "ts" data:
## Start = 15, End = 490
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90992 -0.04728 -0.00450 0.03391 1.82292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0510420 0.0547900 -0.932 0.35204
## log_viral.t 0.0068198 0.0962389 0.071 0.94354
## log_viral.1 -0.0004429 0.1355423 -0.003 0.99739
## log_viral.2 -0.0662456 0.1355423 -0.489 0.62526
## log_viral.3 -0.0267071 0.1355444 -0.197 0.84389
## log_viral.4 0.3559041 0.1355462 2.626 0.00894 **
## log_viral.5 -0.2269657 0.1359995 -1.669 0.09582 .
## log_viral.6 -0.0071780 0.1363630 -0.053 0.95804
## log_viral.7 -0.0289224 0.1364897 -0.212 0.83228
## log_viral.8 -0.0003262 0.1361771 -0.002 0.99809
## log_viral.9 0.1139565 0.1361771 0.837 0.40313
## log_viral.10 -0.0872283 0.1361834 -0.641 0.52215
## log_viral.11 0.0869370 0.1361774 0.638 0.52353
## log_viral.12 -0.0677954 0.1362716 -0.498 0.61907
## log_viral.13 0.0133665 0.1363593 0.098 0.92196
## log_viral.14 -0.0393125 0.0967766 -0.406 0.68477
## log_cases.1 0.9662545 0.0113959 84.790 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1981 on 459 degrees of freedom
## Multiple R-squared: 0.9661, Adjusted R-squared: 0.9649
## F-statistic: 818.1 on 16 and 459 DF, p-value: < 2.2e-16
f_ardl114 <- forecast(mod_ardl114,
x= t(nc_data_test[,5]),
h=14,
interval = TRUE)
rmse(nc_data_test$log_cases,
f_ardl114$forecasts[,2])
## [1] 0.1527168
mae(nc_data_test$log_cases,
f_ardl114$forecasts[,2])
## [1] 0.1284164
checkresiduals(mod_ardl114)
## Time Series:
## Start = 15
## End = 490
## Frequency = 1
## 15 16 17 18 19
## -0.0079361204 0.0749551140 0.0104102776 0.0417587039 0.1788979741
## 20 21 22 23 24
## -0.0197832873 -0.0636556796 0.0659424356 -0.0058961325 0.0563267039
## 25 26 27 28 29
## 0.0722532860 0.0555601394 0.0195105611 0.1191322887 0.0569816684
## 30 31 32 33 34
## 0.0432000544 0.0106782259 0.0277613061 0.0608521145 0.0164457056
## 35 36 37 38 39
## -0.1385073028 0.0055273619 0.0465037029 0.0195600474 -0.0073049436
## 40 41 42 43 44
## 0.0448363228 0.0049317851 -0.0320415286 0.0338699326 0.0305961503
## 45 46 47 48 49
## 0.0283465099 0.0926974719 0.0618128861 -0.0184534334 0.0213206569
## 50 51 52 53 54
## 0.0326426656 -0.0040375544 -0.0371331073 -0.1782426977 0.2204057225
## 55 56 57 58 59
## 0.0104794007 -0.0693380908 -0.0828500659 0.0462878989 0.0246169661
## 60 61 62 63 64
## 0.0262632746 -0.0843961025 -0.0379274320 -0.0720000488 0.0817978511
## 65 66 67 68 69
## -0.0246907811 -0.1745607217 0.0117215188 0.2851422174 0.0443775771
## 70 71 72 73 74
## 0.0028641604 -0.0653787188 0.0414945238 0.1727227919 0.0492103829
## 75 76 77 78 79
## -0.1762951948 -0.0672963539 -0.0814167277 0.1228827473 0.0513663051
## 80 81 82 83 84
## -0.1715105563 -0.0272278816 0.3267267423 0.0269302279 -0.0049594610
## 85 86 87 88 89
## -0.0068720516 -0.1771227030 0.0139272167 0.0124382865 0.0116317455
## 90 91 92 93 94
## -0.0586408875 -0.0057825049 -0.0022346363 0.2057315708 0.0174397517
## 95 96 97 98 99
## 0.0159508215 0.0837310328 0.0630946687 -0.0019086285 0.0872437669
## 100 101 102 103 104
## 0.0692130295 0.0246579464 0.0231690162 0.0438558048 -0.0308327461
## 105 106 107 108 109
## -0.0682791666 0.0288945455 0.0165520992 0.0209345474 0.0194456172
## 110 111 112 113 114
## 0.0187354925 0.0234234992 0.0130892478 0.0212016080 0.0359539623
## 115 116 117 118 119
## 0.0216787007 0.0201897705 -0.0124944339 0.0329172523 -0.0371419702
## 120 121 122 123 124
## -0.0537262902 0.0013843828 0.0164835277 0.0149945975 0.0220603837
## 125 126 127 128 129
## -0.1017259910 0.0188264098 -0.0081172809 -0.0540654425 0.0104045561
## 130 131 132 133 134
## 0.0089156258 -0.0880293066 0.0128322586 -0.1653236580 0.0155740275
## 135 136 137 138 139
## -0.0111191180 0.0019533161 0.0004643858 -0.1051715333 -0.0873028623
## 140 141 142 143 144
## -0.1879690028 -0.0661025606 -0.0561235139 -0.0136130746 -0.0151020048
## 145 146 147 148 149
## -0.6491330093 0.5089412804 0.0198081074 -0.2184427088 -0.0626808175
## 150 151 152 153 154
## -0.0232161815 -0.0247051117 0.3079386518 -0.6193300126 -0.0351904552
## 155 156 157 158 159
## -0.0414229027 0.0188372528 -0.0307096957 -0.0321986260 -0.0149869349
## 160 161 162 163 164
## -0.0036051011 -0.0757256960 -0.0116401080 -0.1742037359 -0.0357920263
## 165 166 167 168 169
## -0.0372032920 -0.2483563235 -0.2813997227 -0.1067490983 -0.0787267436
## 170 171 172 173 174
## 0.0786696808 -0.0471878676 -0.0486563388 0.2077356296 0.0019712878
## 175 176 177 178 179
## -0.0805729466 0.0865198432 0.0129930756 -0.0336060184 -0.0351717909
## 180 181 182 183 184
## -0.5430052770 0.5699702406 -0.0347356633 -0.0104205063 -0.0060264274
## 185 186 187 188 189
## -0.0281139827 -0.0296381870 0.7002595730 -0.1527768573 0.1775209363
## 190 191 192 193 194
## 0.1674719834 0.1528291914 0.0072232150 0.0059096600 0.2073372355
## 195 196 197 198 199
## 0.0335530920 -0.1284625207 0.0521549363 0.1490383312 0.0134896319
## 200 201 202 203 204
## 0.0124702152 0.2319947813 0.1609154434 -0.1409760511 0.1574839305
## 205 206 207 208 209
## 0.0712239389 0.0229084624 0.0220056565 0.1333588061 0.2773868323
## 210 211 212 213 214
## -0.4082967438 -0.0289206932 -0.0188004247 0.0180399290 0.0166556427
## 215 216 217 218 219
## 0.1653146892 -0.2047006295 0.1675126483 0.0762783587 0.0738031871
## 220 221 222 223 224
## 0.0143720963 0.0128985843 0.0468493669 0.0396119258 -0.0621725083
## 225 226 227 228 229
## 0.0147808954 0.0266446386 0.0170979071 0.0158166921 0.1304838681
## 230 231 232 233 234
## 0.0297638686 -0.1115102331 0.0400706930 0.0234368102 0.0175708037
## 235 236 237 238 239
## 0.0161697623 0.0459638561 -0.0108645017 -0.0137342257 -0.0215486015
## 240 241 242 243 244
## -0.0174015080 0.0122976291 0.0108086989 -0.5462422658 0.4987813802
## 245 246 247 248 249
## -0.0827648429 -0.0078687278 -0.0051523814 0.0069010163 0.0054120861
## 250 251 252 253 254
## 0.5476827967 -0.3030223961 -0.0066957590 0.0184288810 0.1092836405
## 255 256 257 258 259
## 0.0172406784 0.0157517482 -0.2118031721 -0.0219490663 -0.0494768935
## 260 261 262 263 264
## -0.0182412713 -0.0355656984 0.0047338360 0.0032449058 -0.0303316544
## 265 266 267 268 269
## -0.0461200114 -0.0402549344 0.0040586207 -0.0396813616 -0.0003193617
## 270 271 272 273 274
## -0.0018082919 -0.0109040051 -0.0518081474 -0.0831792400 0.0242242065
## 275 276 277 278 279
## -0.0054861990 -0.0037181888 -0.0052071191 -0.0785204405 -0.0515469270
## 280 281 282 283 284
## -0.0901820582 -0.0732495831 -0.0398027942 -0.0131189694 -0.0146078997
## 285 286 287 288 289
## -0.1030378317 -0.0585937511 -0.0740603660 -0.0188162420 -0.0889480916
## 290 291 292 293 294
## -0.0213484116 -0.0228373419 -0.0009888652 -0.0583160775 -0.0933343153
## 295 296 297 298 299
## -0.2939240825 0.2093383182 -0.0247814122 -0.0262703424 -0.1015690145
## 300 301 302 303 304
## -0.0390658512 -0.1067096847 0.1278524620 -0.2962888130 -0.0337768716
## 305 306 307 308 309
## -0.0352658018 0.0648706161 -0.0386313636 -0.0412756075 -0.2067728246
## 310 311 312 313 314
## 0.2027474944 -0.0284536161 -0.0299425463 -0.1194382612 -0.0796777732
## 315 316 317 318 319
## -0.0893594924 0.1835312754 -0.2090382615 -0.0333254430 -0.0348143732
## 320 321 322 323 324
## 0.0695995113 -0.1067974520 -0.1118620619 -0.2982037909 -0.3142264635
## 325 326 327 328 329
## -0.0526601978 -0.0541491280 0.2644388950 -0.0093278635 0.0558597065
## 330 331 332 333 334
## 0.2707293092 0.1847381877 -0.0195737102 -0.0210626404 0.1126526669
## 335 336 337 338 339
## 0.0332107496 0.0273795097 0.0511426205 0.0341275014 -0.0080152001
## 340 341 342 343 344
## -0.0095041303 -0.0069758511 -0.0526065691 -0.0957398444 -0.0090761737
## 345 346 347 348 349
## 0.0160888997 -0.0108625075 -0.0123514377 -0.0010008676 -0.0228389005
## 350 351 352 353 354
## -0.0472800585 -0.2545202184 -0.2846204474 -0.0288026761 -0.0302916063
## 355 356 357 358 359
## -0.9058903735 1.5652411290 -0.1628820768 0.3315450181 0.0155505485
## 360 361 362 363 364
## 0.0034116287 0.0019226985 0.7549825649 -0.2684037661 0.2725795109
## 365 366 367 368 369
## 0.1214239086 0.2670232421 0.0389337198 0.0374447896 0.1721576193
## 370 371 372 373 374
## 0.0861561917 0.0188683809 0.1833389820 0.1157649150 0.0514240222
## 375 376 377 378 379
## 0.0499350920 -0.3315783638 0.6859096507 0.0254283685 0.0111584290
## 380 381 382 383 384
## -0.0978447114 0.0527690387 0.0512801085 0.6068872423 -0.3934194425
## 385 386 387 388 389
## -0.0123567000 0.1404074447 0.2065508315 0.0566622114 0.0555163791
## 390 391 392 393 394
## -0.2125527694 0.0638413436 -0.2490112019 -0.1070191973 -0.0657752020
## 395 396 397 398 399
## 0.0397380690 0.0381994992 -0.3181207230 -0.1465143113 0.1600813958
## 400 401 402 403 404
## -0.1376118862 -0.0233191256 0.0146532435 0.0125864130 -0.0450035769
## 405 406 407 408 409
## -0.0729973980 0.1954139556 0.0725111900 -0.0485840740 0.0192594298
## 410 411 412 413 414
## 0.0173593428 -0.0300150667 -0.1064081660 -0.0606890359 -0.1471772732
## 415 416 417 418 419
## -0.0472908167 0.0136989670 0.0117901025 -0.3343997815 -0.0541140700
## 420 421 422 423 424
## 0.0739029076 -0.0423713434 -0.0573320347 0.0012472156 -0.0006758919
## 425 426 427 428 429
## 0.0103248355 -0.0569044785 0.1365386768 -0.0364978247 0.0830236429
## 430 431 432 433 434
## 0.0121966072 0.0103500213 -0.0807190521 -0.1064033790 0.0816416569
## 435 436 437 438 439
## -0.0374279359 -0.0177343901 0.0083650951 0.0066315216 0.1274158456
## 440 441 442 443 444
## 0.0340155770 0.1250497496 0.1538768441 0.1140251474 0.0283837841
## 445 446 447 448 449
## 0.0267832477 0.1310663625 -0.0160997119 0.0922018757 0.0438603288
## 450 451 452 453 454
## -0.0559222034 0.0299940801 0.0285615872 -0.0548322644 -0.0089794018
## 455 456 457 458 459
## -0.2664375111 -0.3134873862 -0.3155900116 -0.0083381840 -0.0094403393
## 460 461 462 463 464
## -0.8998684248 -0.9099201774 1.8229177938 -0.0278178361 -0.0187554169
## 465 466 467 468 469
## -0.0060663639 -0.0070574181 -0.0236574378 0.0089609705 -0.1985607999
## 470 471 472 473 474
## -0.0516989335 -0.0506748450 -0.0188521589 -0.0200424954 -0.0440537621
## 475 476 477 478 479
## -0.0327497766 0.4277819064 -0.0278734106 -0.0275121563 -0.0096476569
## 480 481 482 483 484
## -0.0110513494 -0.0102416409 -0.0353550298 -0.0551953313 -0.0147304285
## 485 486 487 488 489
## -0.0113245502 -0.0152254509 -0.0166016525 0.0249369224 -0.0137193043
## 490
## -0.2448440774
nc_data_test <- cbind(nc_data_test,f_ardl114$forecasts[,2],f_ardl114$forecasts[,1],
f_ardl114$forecasts[,3])
png(filename = "sensitivity_nc_ardl.png",res = 700, units = "cm",
width = 20, height = 10)
ardl_plot <- nc_data_train %>% ggplot(aes(date,log_cases)) +
geom_line() +
geom_ribbon(data = nc_data_test , aes(ymin = f_ardl114$forecasts[,1],
ymax = f_ardl114$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = nc_data_test,aes(date,log_cases,color="Actual")) +
geom_line(data = nc_data_test,aes(date,f_ardl114$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "bottom") + ylab("")
dev.off()
## quartz_off_screen
## 2
exp(f_ardl114 $forecasts[1,2])
## [1] 11.95761
exp(f_ardl114 $forecasts[1,1])
## [1] 8.101852
exp(f_ardl114 $forecasts[1,3])
## [1] 17.72089
exp(f_ardl114 $forecasts[1,2]) - exp(nc_data_test[1,4])
## [1] 0.2743545
exp(f_ardl114 $forecasts[7,2])
## [1] 14.73769
exp(f_ardl114 $forecasts[7,1])
## [1] 5.738535
exp(f_ardl114 $forecasts[7,3])
## [1] 36.01211
exp(f_ardl114$forecasts[7,2]) - exp(nc_data_test[7,4])
## [1] -3.410547
exp(f_ardl114 $forecasts[14,2])
## [1] 17.70536
exp(f_ardl114$forecasts[14,1])
## [1] 5.575139
exp(f_ardl114$forecasts[14,3])
## [1] 56.09214
exp(f_ardl114 $forecasts[14,2]) - exp(nc_data_test[14,4])
## [1] -7.62401
#Distributed lag model
lowest_rmse_dl <- Inf
best_mod_dl <- NULL
for (q in seq(1,14)){
mod <- dlm(log_cases ~ log_viral,
data = nc_data_train,q=q)
f <- forecast(mod, x= t(nc_data_test[,5]),h=14)
forecast_acc <- mae(nc_data_test[,4],
f$forecasts)
if (forecast_acc<lowest_rmse_dl){
lowest_rmse_dl <- forecast_acc
best_mod_dl <-mod
}
}
lowest_rmse_dl #0.622
## [1] 0.5919259
summary(best_mod_dl) #DL(14)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.29091 -0.53312 0.09167 0.43047 2.03724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.7698170 0.2207213 -3.488 0.000534 ***
## log_viral.t 0.0708392 0.3924113 0.181 0.856822
## log_viral.1 0.0005531 0.5526871 0.001 0.999202
## log_viral.2 -0.0656752 0.5526871 -0.119 0.905463
## log_viral.3 -0.0902575 0.5526871 -0.163 0.870349
## log_viral.4 0.2687696 0.5526871 0.486 0.626989
## log_viral.5 0.0715636 0.5543655 0.129 0.897342
## log_viral.6 0.0233671 0.5560317 0.042 0.966497
## log_viral.7 -0.1222001 0.5565320 -0.220 0.826300
## log_viral.8 0.0005348 0.5552756 0.001 0.999232
## log_viral.9 0.1145059 0.5552756 0.206 0.836715
## log_viral.10 0.0233234 0.5552756 0.042 0.966514
## log_viral.11 0.1095497 0.5552756 0.197 0.843689
## log_viral.12 0.0145768 0.5556466 0.026 0.979082
## log_viral.13 0.0508206 0.5560157 0.091 0.927214
## log_viral.14 0.1952651 0.3944549 0.495 0.620819
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8076 on 460 degrees of freedom
## Multiple R-squared: 0.4355, Adjusted R-squared: 0.4171
## F-statistic: 23.66 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1165.17 1235.982
checkresiduals(best_mod_dl)
## 1 2 3 4 5 6
## 1.536593406 1.551576009 1.503886164 1.486720187 1.607319380 1.525131019
## 7 8 9 10 11 12
## 1.401871490 1.412649754 1.350963648 1.355959990 1.374280435 1.375336126
## 13 14 15 16 17 18
## 1.340270000 1.406036663 1.407713604 1.395290258 1.353142299 1.327065848
## 19 20 21 22 23 24
## 1.335006793 1.298236744 1.107782248 1.068069622 1.070411373 1.048108430
## 25 26 27 28 29 30
## 0.997259244 1.000313879 0.963324283 0.890637343 0.886594946 0.879153095
## 31 32 33 34 35 36
## 0.872090716 0.927183748 0.949579678 0.890916913 0.874035580 0.869326150
## 37 38 39 40 41 42
## 0.827833339 0.757023153 0.545059025 0.738942774 0.716320886 0.614672632
## 43 44 45 46 47 48
## 0.503222798 0.524409773 0.525588834 0.525940541 0.415667627 0.355547982
## 49 50 51 52 53 54
## 0.263412225 0.328463759 0.284569382 0.094664284 0.095015991 0.368823153
## 55 56 57 58 59 60
## 0.392589306 0.374067781 0.288208620 0.311857977 0.468315526 0.493547057
## 61 62 63 64 65 66
## 0.292468184 0.207137041 0.110592804 0.221886199 0.257645419 0.071699049
## 67 68 69 70 71 72
## 0.033876328 0.351331202 0.358240280 0.333054258 0.307085786 0.111480896
## 73 74 75 76 77 78
## 0.115904691 0.116256398 0.115836320 0.045121171 0.029678459 0.018584964
## 79 80 81 82 83 84
## 0.215569948 0.219993742 0.220345449 0.288512124 0.333705503 0.312398251
## 85 86 87 88 89 90
## 0.381242644 0.429471028 0.433894823 0.434246530 0.455319782 0.400956742
## 91 92 93 94 95 96
## 0.311009526 0.321551561 0.319133319 0.323557114 0.323908821 0.323585160
## 97 98 99 100 101 102
## 0.327923813 0.321809543 0.324294188 0.341185259 0.345609054 0.345960760
## 103 104 105 106 107 108
## 0.313663019 0.327830253 0.271487922 0.200742797 0.187233589 0.191657384
## 109 110 111 112 113 114
## 0.192009090 0.199461340 0.082839121 0.090732513 0.071696075 0.007091785
## 115 116 117 118 119 120
## 0.011515580 0.011867287 -0.084691182 -0.077166288 -0.248023504 -0.231937149
## 121 122 123 124 125 126
## -0.243348866 -0.238925071 -0.238573364 -0.343822820 -0.427688526 -0.609362545
## 127 128 129 130 131 132
## -0.662759219 -0.704637034 -0.700213239 -0.699861532 -1.333506074 -0.787730300
## 133 134 135 136 137 138
## -0.749477427 -0.950486005 -0.989211645 -0.984787850 -0.984436143 -0.651405916
## 139 140 141 142 143 144
## -1.256919233 -1.257831917 -1.264666022 -1.211271437 -1.206847642 -1.206495935
## 145 146 147 148 149 150
## -1.188897781 -1.160548265 -1.205248274 -1.184074045 -1.326440063 -1.334438506
## 151 152 153 154 155 156
## -1.334183795 -1.545050378 -1.781865161 -1.836023690 -1.866861091 -1.732754075
## 157 158 159 160 161 162
## -1.701025221 -1.700721409 -1.443992009 -1.401718794 -1.443395606 -1.308954457
## 163 164 165 166 167 168
## -1.260139179 -1.292130475 -1.291672229 -1.799009565 -1.176305402 -1.179277836
## 169 170 171 172 173 174
## -1.155137562 -1.130080806 -1.123418340 -1.123008256 -0.392664066 -0.540048580
## 175 176 177 178 179 180
## -0.352125651 -0.183074443 -0.031884634 -0.033014202 -0.032881923 0.168705864
## 181 182 183 184 185 186
## 0.189706464 0.047979883 0.076721592 0.216238175 0.213594953 0.213310121
## 187 188 189 190 191 192
## 0.432565593 0.573412077 0.407552322 0.525367395 0.573217045 0.541321379
## 193 194 195 196 197 198
## 0.540842936 0.651728114 0.903001334 0.460022129 0.400370189 0.363782137
## 199 200 201 202 203 204
## 0.332934265 0.333058933 0.481871860 0.255649960 0.409269991 0.496957823
## 205 206 207 208 209 210
## 0.548900285 0.347292287 0.347665591 0.382024461 0.407945670 0.331239052
## 211 212 213 214 215 216
## 0.316304987 0.331429143 0.412483890 0.412541656 0.527292753 0.537463943
## 217 218 219 220 221 222
## 0.406004024 0.426740914 0.433951963 0.418395655 0.418603265 0.448635783
## 223 224 225 226 227 228
## 0.420814155 0.391068798 0.361120007 0.329769986 0.281579274 0.281930981
## 229 230 231 232 233 234
## -0.274733520 0.232373921 0.140850293 0.127591516 0.117234424 0.121658219
## 235 236 237 238 239 240
## 0.122009926 0.664667100 0.338270240 0.319242174 0.326261086 0.423635816
## 241 242 243 244 245 246
## 0.428059611 0.428411318 0.201242861 0.171557804 0.115374395 0.092602770
## 247 248 249 250 251 252
## 0.053013074 0.057436869 0.057788576 0.024598478 -0.023296574 -0.063682570
## 253 254 255 256 257 258
## -0.058111939 -0.096731358 -0.092307563 -0.091955857 -0.100665107 -0.150021215
## 259 260 261 262 263 264
## -0.229055132 -0.197738339 -0.197450836 -0.193027041 -0.192675335 -0.265602193
## 265 266 267 268 269 270
## -0.309131200 -0.389798693 -0.450531321 -0.476029792 -0.471605997 -0.471254290
## 271 272 273 274 275 276
## -0.559297759 -0.599962693 -0.654694245 -0.652054504 -0.719897776 -0.715473982
## 277 278 279 280 281 282
## -0.715122275 -0.692887335 -0.728766550 -0.798425504 -1.066043323 -0.821629934
## 283 284 285 286 287 288
## -0.817206140 -0.816854433 -0.891766642 -0.901684353 -0.978883482 -0.818635115
## 289 290 291 292 293 294
## -1.088197766 -1.083773972 -1.083422265 -0.982899384 -0.989307289 -0.998115463
## 295 296 297 298 299 300
## -1.171843391 -0.930450552 -0.926026757 -0.925675050 -1.014784302 -1.061162645
## 301 302 303 304 305 306
## -1.115629910 -0.895088156 -1.074820311 -1.070396516 -1.070044810 -0.965244462
## 307 308 309 310 311 312
## -1.040414230 -1.118084229 -1.379194720 -1.647778669 -1.643354874 -1.643003167
## 313 314 315 316 317 318
## -1.324028681 -1.289621514 -1.191160126 -0.880871535 -0.667306988 -0.662883193
## 319 320 321 322 323 324
## -0.662531486 -0.528429716 -0.478331805 -0.435727974 -0.370518493 -0.324786740
## 325 326 327 328 329 330
## -0.320362945 -0.320011239 -0.317096496 -0.359947445 -0.444457906 -0.439172623
## 331 332 333 334 335 336
## -0.409162705 -0.404738910 -0.404387203 -0.392650170 -0.403183856 -0.437775497
## 337 338 339 340 341 342
## -0.678159760 -0.940794454 -0.936370659 -0.936018952 -1.811231256 -0.185814212
## 343 344 345 346 347 348
## -0.343343114 -0.000848807 0.013831312 0.018255107 0.018606814 0.772053143
## 349 350 351 352 353 354
## 0.476651120 0.732228594 0.828306109 1.066478690 1.070902485 1.071254192
## 355 356 357 358 359 360
## 1.206353485 1.250855746 1.226596184 1.367906100 1.436611294 1.441035089
## 361 362 363 364 365 366
## 1.441386795 1.060259803 1.709445524 1.676270617 1.630225501 1.476468974
## 367 368 369 370 371 372
## 1.480892769 1.481244476 2.037238073 1.574126100 1.507732544 1.596623841
## 373 374 375 376 377 378
## 1.748396762 1.697942945 1.697866152 1.429741633 1.447093373 1.150974958
## 379 380 381 382 383 384
## 0.977041114 0.879864019 1.027309129 1.027624127 0.671654076 0.499273671
## 385 386 387 388 389 390
## 0.639327250 0.521937025 0.478084054 0.304646360 0.305806787 0.249435775
## 391 392 393 394 395 396
## 0.166801788 0.355509520 0.430344089 0.366283556 0.429895045 0.430862451
## 397 398 399 400 401 402
## 0.384507750 0.263184454 0.191789518 0.030870869 -0.019281431 0.150064647
## 403 404 405 406 407 408
## 0.150983831 -0.194235131 -0.247649753 -0.171137346 -0.193966235 -0.250361891
## 409 410 411 412 413 414
## -0.232545257 -0.231562172 -0.219525362 -0.275266216 -0.135565791 -0.171699933
## 415 416 417 418 419 420
## -0.088964302 0.028150138 0.029007791 -0.061154063 -0.174078710 -0.095048432
## 421 422 423 424 425 426
## -0.130341489 -0.152091940 -0.098790597 -0.098074107 0.023471879 0.047418264
## 427 428 429 430 431 432
## 0.161670229 0.298407458 0.393178738 0.469642037 0.470159878 0.575000338
## 433 434 435 436 437 438
## 0.529072399 0.593047211 0.605653855 0.518937020 0.538345220 0.538638850
## 439 440 441 442 443 444
## 0.455571381 0.421132727 0.130417922 -0.207275816 -0.525974878 -0.529672662
## 445 446 447 448 449 450
## -0.529829378 -1.420394844 -2.290911786 -0.399258326 -0.445433336 -0.457853386
## 451 452 453 454 455 456
## -0.445247845 -0.445610524 -0.462559236 -0.446234905 -0.638056496 -0.682071998
## 457 458 459 460 461 462
## -0.718082998 -0.800597143 -0.800693401 -0.824778925 -0.836709246 -0.387741136
## 463 464 465 466 467 468
## -0.404803053 -0.425674312 -0.507977759 -0.507763137 -0.506707833 -0.530815066
## 469 470 471 472 473 474
## -0.573940919 -0.569819727 -0.567717078 -0.625579768 -0.625370813 -0.583592938
## 475 476
## -0.581894113 -0.811369602
mod_dl14 <- dlm(log_cases ~ log_viral,
data = nc_data_train,q=14)
summary(mod_dl14)
##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.29091 -0.53312 0.09167 0.43047 2.03724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.7698170 0.2207213 -3.488 0.000534 ***
## log_viral.t 0.0708392 0.3924113 0.181 0.856822
## log_viral.1 0.0005531 0.5526871 0.001 0.999202
## log_viral.2 -0.0656752 0.5526871 -0.119 0.905463
## log_viral.3 -0.0902575 0.5526871 -0.163 0.870349
## log_viral.4 0.2687696 0.5526871 0.486 0.626989
## log_viral.5 0.0715636 0.5543655 0.129 0.897342
## log_viral.6 0.0233671 0.5560317 0.042 0.966497
## log_viral.7 -0.1222001 0.5565320 -0.220 0.826300
## log_viral.8 0.0005348 0.5552756 0.001 0.999232
## log_viral.9 0.1145059 0.5552756 0.206 0.836715
## log_viral.10 0.0233234 0.5552756 0.042 0.966514
## log_viral.11 0.1095497 0.5552756 0.197 0.843689
## log_viral.12 0.0145768 0.5556466 0.026 0.979082
## log_viral.13 0.0508206 0.5560157 0.091 0.927214
## log_viral.14 0.1952651 0.3944549 0.495 0.620819
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8076 on 460 degrees of freedom
## Multiple R-squared: 0.4355, Adjusted R-squared: 0.4171
## F-statistic: 23.66 on 15 and 460 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 1165.17 1235.982
f_dl14 <- forecast(mod_dl14,
x= t(nc_data_test[,5]),
h=14,
interval = TRUE)
rmse(nc_data_test$log_cases,
f_dl14$forecasts[,2])
## [1] 0.6221004
mae(nc_data_test$log_cases,
f_dl14$forecasts[,2])
## [1] 0.5919259
checkresiduals(mod_dl14)
## 1 2 3 4 5 6
## 1.536593406 1.551576009 1.503886164 1.486720187 1.607319380 1.525131019
## 7 8 9 10 11 12
## 1.401871490 1.412649754 1.350963648 1.355959990 1.374280435 1.375336126
## 13 14 15 16 17 18
## 1.340270000 1.406036663 1.407713604 1.395290258 1.353142299 1.327065848
## 19 20 21 22 23 24
## 1.335006793 1.298236744 1.107782248 1.068069622 1.070411373 1.048108430
## 25 26 27 28 29 30
## 0.997259244 1.000313879 0.963324283 0.890637343 0.886594946 0.879153095
## 31 32 33 34 35 36
## 0.872090716 0.927183748 0.949579678 0.890916913 0.874035580 0.869326150
## 37 38 39 40 41 42
## 0.827833339 0.757023153 0.545059025 0.738942774 0.716320886 0.614672632
## 43 44 45 46 47 48
## 0.503222798 0.524409773 0.525588834 0.525940541 0.415667627 0.355547982
## 49 50 51 52 53 54
## 0.263412225 0.328463759 0.284569382 0.094664284 0.095015991 0.368823153
## 55 56 57 58 59 60
## 0.392589306 0.374067781 0.288208620 0.311857977 0.468315526 0.493547057
## 61 62 63 64 65 66
## 0.292468184 0.207137041 0.110592804 0.221886199 0.257645419 0.071699049
## 67 68 69 70 71 72
## 0.033876328 0.351331202 0.358240280 0.333054258 0.307085786 0.111480896
## 73 74 75 76 77 78
## 0.115904691 0.116256398 0.115836320 0.045121171 0.029678459 0.018584964
## 79 80 81 82 83 84
## 0.215569948 0.219993742 0.220345449 0.288512124 0.333705503 0.312398251
## 85 86 87 88 89 90
## 0.381242644 0.429471028 0.433894823 0.434246530 0.455319782 0.400956742
## 91 92 93 94 95 96
## 0.311009526 0.321551561 0.319133319 0.323557114 0.323908821 0.323585160
## 97 98 99 100 101 102
## 0.327923813 0.321809543 0.324294188 0.341185259 0.345609054 0.345960760
## 103 104 105 106 107 108
## 0.313663019 0.327830253 0.271487922 0.200742797 0.187233589 0.191657384
## 109 110 111 112 113 114
## 0.192009090 0.199461340 0.082839121 0.090732513 0.071696075 0.007091785
## 115 116 117 118 119 120
## 0.011515580 0.011867287 -0.084691182 -0.077166288 -0.248023504 -0.231937149
## 121 122 123 124 125 126
## -0.243348866 -0.238925071 -0.238573364 -0.343822820 -0.427688526 -0.609362545
## 127 128 129 130 131 132
## -0.662759219 -0.704637034 -0.700213239 -0.699861532 -1.333506074 -0.787730300
## 133 134 135 136 137 138
## -0.749477427 -0.950486005 -0.989211645 -0.984787850 -0.984436143 -0.651405916
## 139 140 141 142 143 144
## -1.256919233 -1.257831917 -1.264666022 -1.211271437 -1.206847642 -1.206495935
## 145 146 147 148 149 150
## -1.188897781 -1.160548265 -1.205248274 -1.184074045 -1.326440063 -1.334438506
## 151 152 153 154 155 156
## -1.334183795 -1.545050378 -1.781865161 -1.836023690 -1.866861091 -1.732754075
## 157 158 159 160 161 162
## -1.701025221 -1.700721409 -1.443992009 -1.401718794 -1.443395606 -1.308954457
## 163 164 165 166 167 168
## -1.260139179 -1.292130475 -1.291672229 -1.799009565 -1.176305402 -1.179277836
## 169 170 171 172 173 174
## -1.155137562 -1.130080806 -1.123418340 -1.123008256 -0.392664066 -0.540048580
## 175 176 177 178 179 180
## -0.352125651 -0.183074443 -0.031884634 -0.033014202 -0.032881923 0.168705864
## 181 182 183 184 185 186
## 0.189706464 0.047979883 0.076721592 0.216238175 0.213594953 0.213310121
## 187 188 189 190 191 192
## 0.432565593 0.573412077 0.407552322 0.525367395 0.573217045 0.541321379
## 193 194 195 196 197 198
## 0.540842936 0.651728114 0.903001334 0.460022129 0.400370189 0.363782137
## 199 200 201 202 203 204
## 0.332934265 0.333058933 0.481871860 0.255649960 0.409269991 0.496957823
## 205 206 207 208 209 210
## 0.548900285 0.347292287 0.347665591 0.382024461 0.407945670 0.331239052
## 211 212 213 214 215 216
## 0.316304987 0.331429143 0.412483890 0.412541656 0.527292753 0.537463943
## 217 218 219 220 221 222
## 0.406004024 0.426740914 0.433951963 0.418395655 0.418603265 0.448635783
## 223 224 225 226 227 228
## 0.420814155 0.391068798 0.361120007 0.329769986 0.281579274 0.281930981
## 229 230 231 232 233 234
## -0.274733520 0.232373921 0.140850293 0.127591516 0.117234424 0.121658219
## 235 236 237 238 239 240
## 0.122009926 0.664667100 0.338270240 0.319242174 0.326261086 0.423635816
## 241 242 243 244 245 246
## 0.428059611 0.428411318 0.201242861 0.171557804 0.115374395 0.092602770
## 247 248 249 250 251 252
## 0.053013074 0.057436869 0.057788576 0.024598478 -0.023296574 -0.063682570
## 253 254 255 256 257 258
## -0.058111939 -0.096731358 -0.092307563 -0.091955857 -0.100665107 -0.150021215
## 259 260 261 262 263 264
## -0.229055132 -0.197738339 -0.197450836 -0.193027041 -0.192675335 -0.265602193
## 265 266 267 268 269 270
## -0.309131200 -0.389798693 -0.450531321 -0.476029792 -0.471605997 -0.471254290
## 271 272 273 274 275 276
## -0.559297759 -0.599962693 -0.654694245 -0.652054504 -0.719897776 -0.715473982
## 277 278 279 280 281 282
## -0.715122275 -0.692887335 -0.728766550 -0.798425504 -1.066043323 -0.821629934
## 283 284 285 286 287 288
## -0.817206140 -0.816854433 -0.891766642 -0.901684353 -0.978883482 -0.818635115
## 289 290 291 292 293 294
## -1.088197766 -1.083773972 -1.083422265 -0.982899384 -0.989307289 -0.998115463
## 295 296 297 298 299 300
## -1.171843391 -0.930450552 -0.926026757 -0.925675050 -1.014784302 -1.061162645
## 301 302 303 304 305 306
## -1.115629910 -0.895088156 -1.074820311 -1.070396516 -1.070044810 -0.965244462
## 307 308 309 310 311 312
## -1.040414230 -1.118084229 -1.379194720 -1.647778669 -1.643354874 -1.643003167
## 313 314 315 316 317 318
## -1.324028681 -1.289621514 -1.191160126 -0.880871535 -0.667306988 -0.662883193
## 319 320 321 322 323 324
## -0.662531486 -0.528429716 -0.478331805 -0.435727974 -0.370518493 -0.324786740
## 325 326 327 328 329 330
## -0.320362945 -0.320011239 -0.317096496 -0.359947445 -0.444457906 -0.439172623
## 331 332 333 334 335 336
## -0.409162705 -0.404738910 -0.404387203 -0.392650170 -0.403183856 -0.437775497
## 337 338 339 340 341 342
## -0.678159760 -0.940794454 -0.936370659 -0.936018952 -1.811231256 -0.185814212
## 343 344 345 346 347 348
## -0.343343114 -0.000848807 0.013831312 0.018255107 0.018606814 0.772053143
## 349 350 351 352 353 354
## 0.476651120 0.732228594 0.828306109 1.066478690 1.070902485 1.071254192
## 355 356 357 358 359 360
## 1.206353485 1.250855746 1.226596184 1.367906100 1.436611294 1.441035089
## 361 362 363 364 365 366
## 1.441386795 1.060259803 1.709445524 1.676270617 1.630225501 1.476468974
## 367 368 369 370 371 372
## 1.480892769 1.481244476 2.037238073 1.574126100 1.507732544 1.596623841
## 373 374 375 376 377 378
## 1.748396762 1.697942945 1.697866152 1.429741633 1.447093373 1.150974958
## 379 380 381 382 383 384
## 0.977041114 0.879864019 1.027309129 1.027624127 0.671654076 0.499273671
## 385 386 387 388 389 390
## 0.639327250 0.521937025 0.478084054 0.304646360 0.305806787 0.249435775
## 391 392 393 394 395 396
## 0.166801788 0.355509520 0.430344089 0.366283556 0.429895045 0.430862451
## 397 398 399 400 401 402
## 0.384507750 0.263184454 0.191789518 0.030870869 -0.019281431 0.150064647
## 403 404 405 406 407 408
## 0.150983831 -0.194235131 -0.247649753 -0.171137346 -0.193966235 -0.250361891
## 409 410 411 412 413 414
## -0.232545257 -0.231562172 -0.219525362 -0.275266216 -0.135565791 -0.171699933
## 415 416 417 418 419 420
## -0.088964302 0.028150138 0.029007791 -0.061154063 -0.174078710 -0.095048432
## 421 422 423 424 425 426
## -0.130341489 -0.152091940 -0.098790597 -0.098074107 0.023471879 0.047418264
## 427 428 429 430 431 432
## 0.161670229 0.298407458 0.393178738 0.469642037 0.470159878 0.575000338
## 433 434 435 436 437 438
## 0.529072399 0.593047211 0.605653855 0.518937020 0.538345220 0.538638850
## 439 440 441 442 443 444
## 0.455571381 0.421132727 0.130417922 -0.207275816 -0.525974878 -0.529672662
## 445 446 447 448 449 450
## -0.529829378 -1.420394844 -2.290911786 -0.399258326 -0.445433336 -0.457853386
## 451 452 453 454 455 456
## -0.445247845 -0.445610524 -0.462559236 -0.446234905 -0.638056496 -0.682071998
## 457 458 459 460 461 462
## -0.718082998 -0.800597143 -0.800693401 -0.824778925 -0.836709246 -0.387741136
## 463 464 465 466 467 468
## -0.404803053 -0.425674312 -0.507977759 -0.507763137 -0.506707833 -0.530815066
## 469 470 471 472 473 474
## -0.573940919 -0.569819727 -0.567717078 -0.625579768 -0.625370813 -0.583592938
## 475 476
## -0.581894113 -0.811369602
nc_data_test <- cbind(nc_data_test,f_dl14$forecasts[,2],
f_dl14$forecasts[,1],
f_dl14$forecasts[,3])
png(filename = "sensitivity_nc_dl.png",res = 700, units = "cm",
width = 20, height = 10)
dl_plot <- nc_data_train %>% ggplot(aes(date,log_cases)) +
geom_line() +
geom_ribbon(data = nc_data_test , aes(ymin = f_dl14$forecasts[,1],
ymax = f_dl14$forecasts[,3]),
fill = adjustcolor( "red", alpha.f = 0.2)) +
geom_line(data = nc_data_test,aes(date,log_cases,color="Actual")) +
geom_line(data = nc_data_test,aes(date,f_dl14$forecasts[,2],color="Forecasted")) +
scale_colour_manual(values=c("Actual"="cyan", "Forecasted"="red"),
labels=c("Actual", "Forecasted")) +
theme_bw() + theme(legend.position = "none") + ylab("")
dev.off()
## quartz_off_screen
## 2
exp(f_dl14 $forecasts[1,2])
## [1] 26.53398
exp(f_dl14 $forecasts[1,1])
## [1] 5.364831
exp(f_dl14 $forecasts[1,3])
## [1] 141.1164
exp(f_dl14 $forecasts[1,2]) - exp(nc_data_test[1,4])
## [1] 14.85072
exp(f_dl14 $forecasts[7,2])
## [1] 28.45966
exp(f_dl14 $forecasts[7,1])
## [1] 5.764687
exp(f_dl14 $forecasts[7,3])
## [1] 148.9824
exp(f_dl14 $forecasts[7,2]) - exp(nc_data_test[7,4])
## [1] 10.31143
exp(f_dl14 $forecasts[14,2])
## [1] 31.09752
exp(f_dl14 $forecasts[14,1])
## [1] 7.046847
exp(f_dl14 $forecasts[14,3])
## [1] 169.9599
exp(f_dl14 $forecasts[14,2]) - exp(nc_data_test[14,4])
## [1] 5.768146
#forecasting
png(filename = "sensitivity_plots.png", res = 700,
units = "cm", width = 20, height = 27)
grid.arrange(arima_plot,
sarima_plot,
arimax_plot,
sarimax_plot,
dl_plot,
ardl_plot,
ncol=1,
left = text_grob("Logarithm of New COVID-19 cases per 10K", rot = 90, vjust = 1))
dev.off()
## quartz_off_screen
## 2